 5.5.4.1: Solve the inequality: 3  4x > 5. Graph the solution set. (pp. 124...
 5.5.1.1: The ____ intercepts of the equation 9x2 + 4y = 36 are 3. To graph y...
 5.5.5.1: Find f( 1) f(x) = 2x2  x. (pp. 210214)
 5.5.2.1: True or False The quotient of two polynomial expressions is a ratio...
 5.5.6.1: Find the sum and the product of the complex numbers 3  2i and 3 +...
 5.5.3.1: The intercepts of the equation y =  are ____ . (pp. 1 651 66)
 5.1: In 14, determine which functions are polynomial functions. For tho...
 5.5.4.2: True or False The first step in solving the inequality x2 + 4x 2:: ...
 5.5.1.2: True or False The expression 4x3  3.6x2  V2 is a polynomial. (pp....
 5.5.5.2: Factor the expression 6x2 + x  2. (pp. 4955)
 5.5.2.2: What is the quotient and remainder when 3x4  x2 is divided by x3 ...
 5.5.6.2: In the complex number system, solve x2 + 2x + 2 = O. (pp. 1 l 41 16)
 5.5.3.2: If the numerator and the denominator of a rational function have no...
 5.2: In 14, determine which functions are polynomial functions. For tho...
 5.5.4.3: In 340, solve each inequality. (x  5)2(x + 2) < 0
 5.5.1.3: To graph y = x2  4, you would shift the graph of y = x2 _____ a di...
 5.5.5.3: Find the quotient and remainder if 3x4  52 + 7x  4 is divided by ...
 5.5.2.3: Graph y =  . (pp. 1 70171) x
 5.5.6.3: Every polynomial function of odd degree with real coefficients will...
 5.5.3.3: True or False The graph of a polynomial function sometimes has a hole.
 5.3: In 14, determine which functions are polynomial functions. For tho...
 5.5.4.4: In 340, solve each inequality. (x  5)(x + 2f > 0
 5.5.1.4: True or False The xintercepts of the graph of a function y = f(x) ...
 5.5.5.4: Solve the equation x2 + x  3 = O. (pp. 1 0 21 04)
 5.5.2.4: Graph y = 2(x + 1)2  3 using transformations. (pp. 2S2260)
 5.5.6.4: If 3 + 4i is a zero of a polynomial function of degree 5 with real ...
 5.5.3.4: True or False The graph of a rational function never intersects a h...
 5.4: In 14, determine which functions are polynomial functions. For tho...
 5.5.4.5: In 340, solve each inequality. x3  4x2 > 0
 5.5.1.5: The graph of every polynomial function is both ____ and ____.
 5.5.5.5: In the process of polynomial division, ( Divisor) (Quotient) + ____...
 5.5.2.5: The line __ is a horizontal asymptote of R x = 3 ' X + 1
 5.5.6.5: True or False A polynomial function of degree n with real coefficie...
 5.5.3.5: True or False The graph of a rational function sometimes intersects...
 5.5: In 510, graph each function using transformations (shifting, compr...
 5.5.4.6: In 340, solve each inequality. x3 + 8x2 < 0
 5.5.1.6: A real number r for which fer) = 0 is called a(n) ____ of the funct...
 5.5.5.6: When a polynomial function f is divided by x  c, the remainder is ...
 5.5.2.6: The line __ is a vertical asymptote of R(x) = : :
 5.5.6.6: True or False A polynomial function of degree 4 with real coefficie...
 5.5.3.6: True or False The graph of a rational function sometimes has a hole.
 5.6: In 510, graph each function using transformations (shifting, compr...
 5.5.4.7: In 340, solve each inequality. x3  9x :::; 0
 5.5.1.7: If r is a real zero of even multiplicity of a function f, the graph...
 5.5.5.7: If a function f, whose domain is all real numbers, is even and if 4...
 5.5.2.7: For a rational function R, if the degree of the numerator is less t...
 5.5.6.7: In 716, information is given about a polynomial f(x) whose coeffic...
 5.5.3.7: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.7: In 510, graph each function using transformations (shifting, compr...
 5.5.4.8: In 340, solve each inequality. x3  x 2:: 0
 5.5.1.8: True or False The graph of f(x) = x2(x  3) (x + 4) has exactly thr...
 5.5.5.8: True or False Every polynomial function of degree 3 with real coeff...
 5.5.2.8: True or False The domain of every rational function is the set of a...
 5.5.6.8: In 716, information is given about a polynomial f(x) whose coeffic...
 5.5.3.8: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.8: In 510, graph each function using transformations (shifting, compr...
 5.5.4.9: In 340, solve each inequality. 2x3 > 8x2
 5.5.1.9: True or False The xintercepts of the graph of a polynomial functio...
 5.5.5.9: True or False The only potential rational zeros of f(x) = 2x5  x3 ...
 5.5.2.9: True or False If an asymptote is neither horizontal nor vertical, i...
 5.5.6.9: In 716, information is given about a polynomial f(x) whose coeffic...
 5.5.3.9: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.9: In 510, graph each function using transformations (shifting, compr...
 5.5.4.10: In 340, solve each inequality. 3x3 < 15x2
 5.5.1.10: True or False End behavior: the graph of the function f(x) = 3x 4 ...
 5.5.5.10: True or False If f is a polynomial function of degree 4 and if f(2)...
 5.5.2.10: True or False If the degree of the numerator of a rational function...
 5.5.6.10: In 716, information is given about a polynomial f(x) whose coeffic...
 5.5.3.10: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.10: In 510, graph each function using transformations (shifting, compr...
 5.5.4.11: In 340, solve each inequality. (x  1 )(x2 + X + 4) 2:: 0
 5.5.1.11: In 1122, determine which functions are polynomial functions. For t...
 5.5.5.11: In 1120, use the Remainder Theorem to find the remainder when f(x)...
 5.5.2.11: In 1122, find the domain of each rational function. R(x) =  12 R...
 5.5.6.11: In 716, information is given about a polynomial f(x) whose coeffic...
 5.5.3.11: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.11: In 1118: (a) Find the x and yintercepts of each polynomial funct...
 5.5.4.12: In 340, solve each inequality. (x + 2) (x2  X + 1) 2:: 0
 5.5.1.12: In 1122, determine which functions are polynomial functions. For t...
 5.5.5.12: In 1120, use the Remainder Theorem to find the remainder when f(x)...
 5.5.2.12: In 1122, find the domain of each rational function. ( ) . x =3+x
 5.5.6.12: In 716, information is given about a polynomial f(x) whose coeffic...
 5.5.3.12: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.12: In 1118: (a) Find the x and yintercepts of each polynomial funct...
 5.5.4.13: In 340, solve each inequality. (x  l)(x  2)(x  3) :::; 0
 5.5.1.13: In 1122, determine which functions are polynomial functions. For t...
 5.5.5.13: In 1120, use the Remainder Theorem to find the remainder when f(x)...
 5.5.2.13: In 1122, find the domain of each rational function. H(x) =4x2(x ...
 5.5.6.13: In 716, information is given about a polynomial f(x) whose coeffic...
 5.5.3.13: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.13: In 1118: (a) Find the x and yintercepts of each polynomial funct...
 5.14: In 1118: (a) Find the x and yintercepts of each polynomial funct...
 5.5.4.14: In 340, solve each inequality. (x + l)(x + 2)(x + 3) :::; 0
 5.5.1.14: In 1122, determine which functions are polynomial functions. For t...
 5.5.5.14: In 1120, use the Remainder Theorem to find the remainder when f(x)...
 5.5.2.14: In 1122, find the domain of each rational function. G(x) = (x + 3)...
 5.5.6.14: In 716, information is given about a polynomial f(x) whose coeffic...
 5.5.3.14: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.15: In 1118: (a) Find the x and yintercepts of each polynomial funct...
 5.5.4.15: In 340, solve each inequality. x3  2x2  3x > 0
 5.5.1.15: In 1122, determine which functions are polynomial functions. For t...
 5.5.5.15: In 1120, use the Remainder Theorem to find the remainder when f(x)...
 5.5.2.15: In 1122, find the domain of each rational function. F ( x) = 2'...
 5.5.6.15: In 716, information is given about a polynomial f(x) whose coeffic...
 5.5.3.15: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.16: In 1118: (a) Find the x and yintercepts of each polynomial funct...
 5.5.4.16: In 340, solve each inequality. x3 + 2x2  3x > 0
 5.5.1.16: In 1122, determine which functions are polynomial functions. For t...
 5.5.5.16: In 1120, use the Remainder Theorem to find the remainder when f(x)...
 5.5.2.16: In 1122, find the domain of each rational function. Q ( x) = 3x...
 5.5.6.16: In 716, information is given about a polynomial f(x) whose coeffic...
 5.5.3.16: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.17: In 1118: (a) Find the x and yintercepts of each polynomial funct...
 5.5.4.17: In 340, solve each inequality. x4 > x2
 5.5.1.17: In 1122, determine which functions are polynomial functions. For t...
 5.5.5.17: In 1120, use the Remainder Theorem to find the remainder when f(x)...
 5.5.2.17: In 1122, find the domain of each rational function. R(x) = X 3  8
 5.5.6.17: In 1722, form a polynomial f(x) with real coefficients having the ...
 5.5.3.17: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.18: In 1118: (a) Find the x and yintercepts of each polynomial funct...
 5.5.4.18: In 340, solve each inequality. X4 < 9x2
 5.5.1.18: In 1122, determine which functions are polynomial functions. For t...
 5.5.5.18: In 1120, use the Remainder Theorem to find the remainder when f(x)...
 5.5.2.18: In 1122, find the domain of each rational function. R(x) = 4x  I
 5.5.6.18: In 1722, form a polynomial f(x) with real coefficients having the ...
 5.5.3.18: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.19: In 1922, find the domain of each rational function. Find any horiz...
 5.5.4.19: In 340, solve each inequality. X4 > 1
 5.5.1.19: In 1122, determine which functions are polynomial functions. For t...
 5.5.5.19: In 1120, use the Remainder Theorem to find the remainder when f(x)...
 5.5.2.19: In 1122, find the domain of each rational function. H(x) =3x2 + Xx...
 5.5.6.19: In 1722, form a polynomial f(x) with real coefficients having the ...
 5.5.3.19: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.20: In 1922, find the domain of each rational function. Find any horiz...
 5.5.4.20: In 340, solve each inequality. x3 > 1
 5.5.1.20: In 1122, determine which functions are polynomial functions. For t...
 5.5.5.20: In 1120, use the Remainder Theorem to find the remainder when f(x)...
 5.5.2.20: In 1122, find the domain of each rational function. G(x) =X + 1
 5.5.6.20: In 1722, form a polynomial f(x) with real coefficients having the ...
 5.5.3.20: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.21: In 1922, find the domain of each rational function. Find any horiz...
 5.5.4.21: In 340, solve each inequality. x + 1 > 0x  I
 5.5.1.21: In 1122, determine which functions are polynomial functions. For t...
 5.5.5.21: In 2132, tell the maximum number of real zeros that each polynomia...
 5.5.2.21: In 1122, find the domain of each rational function. R(x) = 2'4...
 5.5.6.21: In 1722, form a polynomial f(x) with real coefficients having the ...
 5.5.3.21: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.22: In 1922, find the domain of each rational function. Find any horiz...
 5.5.4.22: In 340, solve each inequality. X  3>0x + 1
 5.5.1.22: In 1122, determine which functions are polynomial functions. For t...
 5.5.5.22: In 2132, tell the maximum number of real zeros that each polynomia...
 5.5.2.22: In 1122, find the domain of each rational function. F (x) = '...
 5.5.6.22: In 1722, form a polynomial f(x) with real coefficients having the ...
 5.5.3.22: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.23: In 2334, discuss each rational function following the seven steps ...
 5.5.4.23: In 340, solve each inequality. x  1)(x + 1) :::; 0x
 5.5.1.23: In 2336, use transformations of the graph of y = X4 or y = x5 to g...
 5.5.5.23: In 2132, tell the maximum number of real zeros that each polynomia...
 5.5.2.23: In 2328, use the graph shown to find: (a) The domain and range of ...
 5.5.6.23: In 2330, use the given zero to find the remaining zeros of each fu...
 5.5.3.23: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.24: In 2334, discuss each rational function following the seven steps ...
 5.5.4.24: In 340, solve each inequality. (x  3)(x + 2):::; 0x  I
 5.5.1.24: In 2336, use transformations of the graph of y = X4 or y = x5 to g...
 5.5.5.24: In 2132, tell the maximum number of real zeros that each polynomia...
 5.5.2.24: In 2328, use the graph shown to find: (a) The domain and range of ...
 5.5.6.24: In 2330, use the given zero to find the remaining zeros of each fu...
 5.5.3.24: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.25: In 2334, discuss each rational function following the seven steps ...
 5.5.4.25: In 340, solve each inequality. (x  2)22 2:: 0x  I
 5.5.1.25: In 2336, use transformations of the graph of y = X4 or y = x5 to g...
 5.5.5.25: In 2132, tell the maximum number of real zeros that each polynomia...
 5.5.2.25: In 2328, use the graph shown to find: (a) The domain and range of ...
 5.5.6.25: In 2330, use the given zero to find the remaining zeros of each fu...
 5.5.3.25: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.26: In 2334, discuss each rational function following the seven steps ...
 5.5.4.26: In 340, solve each inequality. (x + 5)2 2:: 0 x2  4
 5.5.1.26: In 2336, use transformations of the graph of y = X4 or y = x5 to g...
 5.5.5.26: In 2132, tell the maximum number of real zeros that each polynomia...
 5.5.2.26: In 2328, use the graph shown to find: (a) The domain and range of ...
 5.5.6.26: In 2330, use the given zero to find the remaining zeros of each fu...
 5.5.3.26: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.27: In 2334, discuss each rational function following the seven steps ...
 5.5.4.27: In 340, solve each inequality. 6 6 x  ) < x
 5.5.1.27: In 2336, use transformations of the graph of y = X4 or y = x5 to g...
 5.5.5.27: In 2132, tell the maximum number of real zeros that each polynomia...
 5.5.2.27: In 2328, use the graph shown to find: (a) The domain and range of ...
 5.5.6.27: In 2330, use the given zero to find the remaining zeros of each fu...
 5.5.3.27: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.28: In 2334, discuss each rational function following the seven steps ...
 5.5.4.28: In 340, solve each inequality. x+ <7x
 5.5.1.28: In 2336, use transformations of the graph of y = X4 or y = x5 to g...
 5.5.5.28: In 2132, tell the maximum number of real zeros that each polynomia...
 5.5.2.28: In 2328, use the graph shown to find: (a) The domain and range of ...
 5.5.6.28: In 2330, use the given zero to find the remaining zeros of each fu...
 5.5.3.28: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.29: In 2334, discuss each rational function following the seven steps ...
 5.5.4.29: In 340, solve each inequality. x + 4 1 x2
 5.5.1.29: In 2336, use transformations of the graph of y = X4 or y = x5 to g...
 5.5.5.29: In 2132, tell the maximum number of real zeros that each polynomia...
 5.5.2.29: In 2940, graph each rational function using transformations. F(x) ...
 5.5.6.29: In 2330, use the given zero to find the remaining zeros of each fu...
 5.5.3.29: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.30: In 2334, discuss each rational function following the seven steps ...
 5.5.4.30: In 340, solve each inequality. x + 2 1x4
 5.5.1.30: In 2336, use transformations of the graph of y = X4 or y = x5 to g...
 5.5.5.30: In 2132, tell the maximum number of real zeros that each polynomia...
 5.5.2.30: In 2940, graph each rational function using transformations. Q(x) ...
 5.5.6.30: In 2330, use the given zero to find the remaining zeros of each fu...
 5.5.3.30: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.31: In 2334, discuss each rational function following the seven steps ...
 5.5.4.31: In 340, solve each inequality. 3x  5 2 x+2
 5.5.1.31: In 2336, use transformations of the graph of y = X4 or y = x5 to g...
 5.5.5.31: In 2132, tell the maximum number of real zeros that each polynomia...
 5.5.2.31: In 2940, graph each rational function using transformations. R(x) ...
 5.5.6.31: In 3140, find the complex zeros of each polynomial function. Write...
 5.5.3.31: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.32: In 2334, discuss each rational function following the seven steps ...
 5.5.4.32: In 340, solve each inequality. x  4  1 2x + 4
 5.5.1.32: In 2336, use transformations of the graph of y = X4 or y = x5 to g...
 5.5.5.32: In 2132, tell the maximum number of real zeros that each polynomia...
 5.5.2.32: In 2940, graph each rational function using transformations. R(x) ...
 5.5.6.32: In 3140, find the complex zeros of each polynomial function. Write...
 5.5.3.32: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.33: In 2334, discuss each rational function following the seven steps ...
 5.5.4.33: In 340, solve each inequality. 1 2x  2<3x  9
 5.5.1.33: In 2336, use transformations of the graph of y = X4 or y = x5 to g...
 5.5.5.33: In 3344, list the potential rational zeros of each polynomial func...
 5.5.2.33: In 2940, graph each rational function using transformations. H ( x...
 5.5.6.33: In 3140, find the complex zeros of each polynomial function. Write...
 5.5.3.33: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.34: In 2334, discuss each rational function following the seven steps ...
 5.5.4.34: In 340, solve each inequality. 5 3 x3 >x+1
 5.5.1.34: In 2336, use transformations of the graph of y = X4 or y = x5 to g...
 5.5.5.34: In 3344, list the potential rational zeros of each polynomial func...
 5.5.2.34: In 2940, graph each rational function using transformations. G(x) ...
 5.5.6.34: In 3140, find the complex zeros of each polynomial function. Write...
 5.5.3.34: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.35: In 3544, solve each inequality. Graph the solution set. x3 + x2 < ...
 5.5.4.35: In 340, solve each inequality. 2x +5 x+1 x+1>xI
 5.5.1.35: In 2336, use transformations of the graph of y = X4 or y = x5 to g...
 5.5.5.35: In 3344, list the potential rational zeros of each polynomial func...
 5.5.2.35: In 2940, graph each rational function using transformations. R(x) ...
 5.5.6.35: In 3140, find the complex zeros of each polynomial function. Write...
 5.5.3.35: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.36: In 3544, solve each inequality. Graph the solution set. x3 + 4x2 2...
 5.5.4.36: In 340, solve each inequality. 1 3 x+2 >x+1
 5.5.1.36: In 2336, use transformations of the graph of y = X4 or y = x5 to g...
 5.5.5.36: In 3344, list the potential rational zeros of each polynomial func...
 5.5.2.36: In 2940, graph each rational function using transformations. R(x) ...
 5.5.6.36: In 3140, find the complex zeros of each polynomial function. Write...
 5.5.3.36: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.37: In 3544, solve each inequality. Graph the solution set. 6 2: 1x + 3
 5.5.4.37: In 340, solve each inequality. x2(3 + x)(x + 4) 0 (x + 5)(x  1)
 5.5.1.37: In 3744, form a polynomial whose real zeros and degree are given. ...
 5.5.5.37: In 3344, list the potential rational zeros of each polynomial func...
 5.5.2.37: In 2940, graph each rational function using transformations. G(x) ...
 5.5.6.37: In 3140, find the complex zeros of each polynomial function. Write...
 5.5.3.37: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.38: In 3544, solve each inequality. Graph the solution set. 2 1 _ 3x < 1
 5.5.4.38: In 340, solve each inequality. (x2 + l)(x  2) 0 (x  l)(x + 1)
 5.5.1.38: In 3744, form a polynomial whose real zeros and degree are given. ...
 5.5.5.38: In 3344, list the potential rational zeros of each polynomial func...
 5.5.2.38: In 2940, graph each rational function using transformations. F(x) ...
 5.5.6.38: In 3140, find the complex zeros of each polynomial function. Write...
 5.5.3.38: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.39: In 3544, solve each inequality. Graph the solution set. 2x  6< 2 ...
 5.5.4.39: In 340, solve each inequality. (3  x)3(2x + 1) 3 < 0x  I
 5.5.1.39: In 3744, form a polynomial whose real zeros and degree are given. ...
 5.5.5.39: In 3344, list the potential rational zeros of each polynomial func...
 5.5.2.39: In 2940, graph each rational function using transformations. R (x)...
 5.5.6.39: In 3140, find the complex zeros of each polynomial function. Write...
 5.5.3.39: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.40: In 3544, solve each inequality. Graph the solution set. 3  2x....
 5.5.4.40: In 340, solve each inequality. (2  x)3(3x  2):3: < 0X + 1
 5.5.1.40: In 3744, form a polynomial whose real zeros and degree are given. ...
 5.5.5.40: In 3344, list the potential rational zeros of each polynomial func...
 5.5.2.40: In 2940, graph each rational function using transformations. R(x) ...
 5.5.6.40: In 3140, find the complex zeros of each polynomial function. Write...
 5.5.3.40: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.5.3.41: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.41: In 3544, solve each inequality. Graph the solution set. (x  2)(x ...
 5.5.4.41: For what positive numbers will the cube of a number exceed four tim...
 5.5.1.41: In 3744, form a polynomial whose real zeros and degree are given. ...
 5.5.5.41: In 3344, list the potential rational zeros of each polynomial func...
 5.5.2.41: In 4152, find the vertical, horizontal, and oblique asymptotes, if...
 5.5.6.41: In 41 and 42, explain why the facts given are contradictory. f(x) i...
 5.5.3.42: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.42: In 3544, solve each inequality. Graph the solution set. x + 1 . ::...
 5.5.4.42: For what positive numbers will the cube of a number be less than th...
 5.5.1.42: In 3744, form a polynomial whose real zeros and degree are given. ...
 5.5.5.42: In 3344, list the potential rational zeros of each polynomial func...
 5.5.2.42: In 4152, find the vertical, horizontal, and oblique asymptotes, if...
 5.5.6.42: In 41 and 42, explain why the facts given are contradictory. f(x) i...
 5.5.3.43: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.43: In 3544, solve each inequality. Graph the solution set. x2  8x + ...
 5.5.4.43: What is the domain of the function f(x) = ?
 5.5.1.43: In 3744, form a polynomial whose real zeros and degree are given. ...
 5.5.5.43: In 3344, list the potential rational zeros of each polynomial func...
 5.5.2.43: In 4152, find the vertical, horizontal, and oblique asymptotes, if...
 5.5.6.43: f(x) is a polynomial of degree 4 whose coefficients are real number...
 5.5.3.44: In 744, follow Steps 1 through 7 on page 355 to analyze the graph ...
 5.44: In 3544, solve each inequality. Graph the solution set. x(x2 + X ...
 5.5.4.44: What is the domain of the function f(x) = V  3?
 5.5.1.44: In 3744, form a polynomial whose real zeros and degree are given. ...
 5.5.5.44: In 3344, list the potential rational zeros of each polynomial func...
 5.5.2.44: In 4152, find the vertical, horizontal, and oblique asymptotes, if...
 5.5.6.44: f(x) is a polynomial of degree 4 whose coefficients are real number...
 5.5.3.45: In 4548, find a rational function that might have the given graph....
 5.45: In 4548, find the remainder R when f(x) is divided by g(x). Is g a...
 5.5.4.45: What is the domain of the function f(x) = ) x  2? x + 4
 5.5.1.45: In 4556, for each polynomial function: (a) List each real zero and...
 5.5.5.45: In 4556, use the Rational Zeros Theorem to find all the real zeros...
 5.5.2.45: In 4152, find the vertical, horizontal, and oblique asymptotes, if...
 5.5.3.46: In 4548, find a rational function that might have the given graph....
 5.46: In 4548, find the remainder R when f(x) is divided by g(x). Is g a...
 5.5.4.46: What is the domain of the function f(x) = ) x  1 ? x+4
 5.5.1.46: In 4556, for each polynomial function: (a) List each real zero and...
 5.5.5.46: In 4556, use the Rational Zeros Theorem to find all the real zeros...
 5.5.2.46: In 4152, find the vertical, horizontal, and oblique asymptotes, if...
 5.5.3.47: In 4548, find a rational function that might have the given graph....
 5.47: In 4548, find the remainder R when f(x) is divided by g(x). Is g a...
 5.5.4.47: In 4750, determine where the graph of f is below the graph of g by...
 5.5.1.47: In 4556, for each polynomial function: (a) List each real zero and...
 5.5.5.47: In 4556, use the Rational Zeros Theorem to find all the real zeros...
 5.5.2.47: In 4152, find the vertical, horizontal, and oblique asymptotes, if...
 5.5.3.48: In 4548, find a rational function that might have the given graph....
 5.48: In 4548, find the remainder R when f(x) is divided by g(x). Is g a...
 5.5.4.48: In 4750, determine where the graph of f is below the graph of g by...
 5.5.1.48: In 4556, for each polynomial function: (a) List each real zero and...
 5.5.5.48: In 4556, use the Rational Zeros Theorem to find all the real zeros...
 5.5.2.48: In 4152, find the vertical, horizontal, and oblique asymptotes, if...
 5.5.3.49: Drug Concentration The concentration C of a certain drug in a patie...
 5.49: Find the value of f(x) = 12x6  8x4 + 1 at x = 4.
 5.5.4.49: In 4750, determine where the graph of f is below the graph of g by...
 5.5.1.49: In 4556, for each polynomial function: (a) List each real zero and...
 5.5.5.49: In 4556, use the Rational Zeros Theorem to find all the real zeros...
 5.5.2.49: In 4152, find the vertical, horizontal, and oblique asymptotes, if...
 5.5.3.50: Drug Concentration The concentration C of a certain drug in a patie...
 5.50: Find the value of f(x) =  16x3 + 1 8x 2  X + 2 at x = 2.
 5.5.4.50: In 4750, determine where the graph of f is below the graph of g by...
 5.5.1.50: In 4556, for each polynomial function: (a) List each real zero and...
 5.5.5.50: In 4556, use the Rational Zeros Theorem to find all the real zeros...
 5.5.2.50: In 4152, find the vertical, horizontal, and oblique asymptotes, if...
 5.5.3.51: Minimum Cost A rectangular area adjacent to a river is to be fenced...
 5.51: In 51 and 52, use Descartes ' Rule of Signs to determine how many p...
 5.5.4.51: Average Cost Suppose that the daily cost C of manufacturing bicycle...
 5.5.1.51: In 4556, for each polynomial function: (a) List each real zero and...
 5.5.5.51: In 4556, use the Rational Zeros Theorem to find all the real zeros...
 5.5.2.51: In 4152, find the vertical, horizontal, and oblique asymptotes, if...
 5.5.3.52: Doppler Effect The Doppler effect (named after Christian Doppler) i...
 5.52: In 51 and 52, use Descartes ' Rule of Signs to determine how many p...
 5.5.4.52: Average Cost See 51. Suppose that the government imposes a $1000 pe...
 5.5.1.52: In 4556, for each polynomial function: (a) List each real zero and...
 5.5.5.52: In 4556, use the Rational Zeros Theorem to find all the real zeros...
 5.5.2.52: In 4152, find the vertical, horizontal, and oblique asymptotes, if...
 5.5.3.53: Minimizing Surface Area United Parcel Service has contracted you to...
 5.53: List all the potential rational zeros of f(x) = 12x8  x7 + 6x4  x...
 5.5.4.53: Bungee "umping Originating on Pentecost Island in the Pacific,the p...
 5.5.1.53: In 4556, for each polynomial function: (a) List each real zero and...
 5.5.5.53: In 4556, use the Rational Zeros Theorem to find all the real zeros...
 5.5.2.53: Gravity In physics, it is established that the acceleration due to ...
 5.5.3.54: Minimizing Surface Area United Parcel Service has contracted you to...
 5.54: List all the potential rational zeros of f(x) = 6x5 + X 4 + 2x3  ...
 5.5.4.54: Gravitational Force According to Newton's Law of universal gravitat...
 5.5.1.54: In 4556, for each polynomial function: (a) List each real zero and...
 5.5.5.54: In 4556, use the Rational Zeros Theorem to find all the real zeros...
 5.5.2.54: Population Model A rare species of insect was discovered in the Ama...
 5.5.3.55: Cost of a Can A can in the shape of a right circular cylinder is re...
 5.55: In 5560, use the Rational Zeros Theorem 10 find all the real zeros...
 5.5.4.55: Make up an inequality that has no solution. Make up one that has ex...
 5.5.1.55: In 4556, for each polynomial function: (a) List each real zero and...
 5.5.5.55: In 4556, use the Rational Zeros Theorem to find all the real zeros...
 5.5.2.55: R esistance in Parallel Circuits From Ohm's law for circuits, it fo...
 5.5.3.56: Material Needed to Make a Drum A steel drum in the shape of a right...
 5.56: In 5560, use the Rational Zeros Theorem 10 find all the real zeros...
 5.5.4.56: The inequality X4 + 1 < 5 has no solution. Explain why.
 5.5.1.56: In 4556, for each polynomial function: (a) List each real zero and...
 5.5.5.56: In 4556, use the Rational Zeros Theorem to find all the real zeros...
 5.5.2.56: Newton's Method In calculus you will learn that, if p(x) = a"x " + ...
 5.5.3.57: Graph each of the following functions: x21 x31 y= xI y= x  I X4...
 5.57: In 5560, use the Rational Zeros Theorem 10 find all the real zeros...
 5.5.4.57: A student attempted to solve the Inequality  0 by x  3 multiplyi...
 5.5.1.57: In 5760, identify which of the graphs could be the graph of a poly...
 5.5.5.57: In 5768, solve each equation in the real number system . x4  x3 +...
 5.5.2.57: If the graph of a rational function R has the vertical asymptote x ...
 5.5.3.58: Graph each of the following functions: x 2 y= xI X 4 y= xI x 6 ...
 5.58: In 5560, use the Rational Zeros Theorem 10 find all the real zeros...
 5.5.4.58: Write a rational inequality whose solution set is {xl 3 < x 5J.
 5.5.1.58: In 5760, identify which of the graphs could be the graph of a poly...
 5.5.5.58: In 5768, solve each equation in the real number system . 2x3 + 3x2...
 5.5.2.58: If the graph of a rational function R has the horizontal asymptote ...
 5.5.3.59: Write a few paragraphs that provide a general strategy for graphing...
 5.59: In 5560, use the Rational Zeros Theorem 10 find all the real zeros...
 5.5.1.59: In 5760, identify which of the graphs could be the graph of a poly...
 5.5.5.59: In 5768, solve each equation in the real number system . 3x3 + 4x2...
 5.5.2.59: Can the graph of a rational function have both a horizontal and an ...
 5.5.3.60: Create a rational function that has the following characteristics: ...
 5.60: In 5560, use the Rational Zeros Theorem 10 find all the real zeros...
 5.5.1.60: In 5760, identify which of the graphs could be the graph of a poly...
 5.5.5.60: In 5768, solve each equation in the real number system . 2x3  3x2...
 5.5.2.60: Make up a rational function that has y = 2x + 1 as an oblique asymp...
 5.5.3.61: Create a rational function that has the following characteristics: ...
 5.61: In 6164, solve each equation in the real number system. 2X4 + 2x3...
 5.5.1.61: In 6164, decide which of the polynomial functions in the list migh...
 5.5.5.61: In 5768, solve each equation in the real number system . 3x3  x2 ...
 5.5.3.62: Create a rational function with the following characteristics: thre...
 5.62: In 6164, solve each equation in the real number system. 3x4 + 3x3...
 5.5.1.62: In 6164, decide which of the polynomial functions in the list migh...
 5.5.5.62: In 5768, solve each equation in the real number system . 2x3  l l...
 5.63: In 6164, solve each equation in the real number system. 2X4 + 7 x...
 5.5.1.63: In 6164, decide which of the polynomial functions in the list migh...
 5.5.5.63: In 5768, solve each equation in the real number system . X4 + 4x3 ...
 5.64: In 6164, solve each equation in the real number system. 2X4 + 7x3...
 5.5.1.64: In 6164, decide which of the polynomial functions in the list migh...
 5.5.5.64: In 5768, solve each equation in the real number system . X4  2x3 ...
 5.65: In 6568, find bounds 10 the real zeros of each polynomial function...
 5.5.1.65: In 6588: (a) Find the x and yintercepts of each polynomial funct...
 5.5.5.65: In 5768, solve each equation in the real number system . O "3 x +...
 5.66: In 6568, find bounds 10 the real zeros of each polynomial function...
 5.5.1.66: In 6588: (a) Find the x and yintercepts of each polynomial funct...
 5.5.5.66: In 5768, solve each equation in the real number system . x3 + x2 ...
 5.67: In 6568, find bounds 10 the real zeros of each polynomial function...
 5.5.1.67: In 6588: (a) Find the x and yintercepts of each polynomial funct...
 5.5.5.67: In 5768, solve each equation in the real number system . 2x4  19x...
 5.68: In 6568, find bounds 10 the real zeros of each polynomial function...
 5.5.1.68: In 6588: (a) Find the x and yintercepts of each polynomial funct...
 5.5.5.68: In 5768, solve each equation in the real number system . 2x4 + x3 ...
 5.69: In 6972, use the Intermediate Value Theorem to show that each poly...
 5.5.1.69: In 6588: (a) Find the x and yintercepts of each polynomial funct...
 5.5.5.69: In 6980, graph each polynomial function. f(x) = x3 + 2x2  5x  6
 5.70: In 6972, use the Intermediate Value Theorem to show that each poly...
 5.5.1.70: In 6588: (a) Find the x and yintercepts of each polynomial funct...
 5.5.5.70: In 6980, graph each polynomial function. f(x) = x3 + 8x2 + 1 1x  20
 5.71: In 6972, use the Intermediate Value Theorem to show that each poly...
 5.5.1.71: In 6588: (a) Find the x and yintercepts of each polynomial funct...
 5.5.5.71: In 6980, graph each polynomial function. f(x) = 2x3  x2 + 2x  1
 5.72: In 6972, use the Intermediate Value Theorem to show that each poly...
 5.5.1.72: In 6588: (a) Find the x and yintercepts of each polynomial funct...
 5.5.5.72: In 6980, graph each polynomial function. f(x) = 2x3 + x2 + 2x + 1
 5.73: In 7376, each polynomial has exactly one positive zero. Approximat...
 5.5.1.73: In 6588: (a) Find the x and yintercepts of each polynomial funct...
 5.5.5.73: In 6980, graph each polynomial function. f ( x) = X4 + x2  2
 5.74: In 7376, each polynomial has exactly one positive zero. Approximat...
 5.5.1.74: In 6588: (a) Find the x and yintercepts of each polynomial funct...
 5.5.5.74: In 6980, graph each polynomial function. f(x) = X4  3x2  4
 5.75: In 7376, each polynomial has exactly one positive zero. Approximat...
 5.5.1.75: In 6588: (a) Find the x and yintercepts of each polynomial funct...
 5.5.5.75: In 6980, graph each polynomial function. f(x) = 4X4 + 7x2  2
 5.76: In 7376, each polynomial has exactly one positive zero. Approximat...
 5.5.1.76: In 6588: (a) Find the x and yintercepts of each polynomial funct...
 5.5.5.76: In 6980, graph each polynomial function. f(x) = 4X4 + 15x2  4
 5.77: In 7780, information is given about a complex polynomial f(x) whos...
 5.5.1.77: In 6588: (a) Find the x and yintercepts of each polynomial funct...
 5.5.5.77: In 6980, graph each polynomial function. f(x) = X4 + x3  3x2  X + 2
 5.78: In 7780, information is given about a complex polynomial f(x) whos...
 5.5.1.78: In 6588: (a) Find the x and yintercepts of each polynomial funct...
 5.5.5.78: In 6980, graph each polynomial function. f(x) = X4  x3  6x2 + 4x...
 5.79: In 7780, information is given about a complex polynomial f(x) whos...
 5.5.1.79: In 6588: (a) Find the x and yintercepts of each polynomial funct...
 5.5.5.79: In 6980, graph each polynomial function. f(x) = 4x5  8x4  X + 2
 5.80: In 7780, information is given about a complex polynomial f(x) whos...
 5.5.1.80: In 6588: (a) Find the x and yintercepts of each polynomial funct...
 5.5.5.80: In 6980, graph each polynomial function. f(x) = 4x5 + 12x4  X  3
 5.81: In 8188, find the complex zeros of each polynomial function f(x). ...
 5.5.1.81: In 6588: (a) Find the x and yintercepts of each polynomial funct...
 5.5.5.81: In 8188, find bounds on the real zeros of each polynomial function...
 5.82: In 8188, find the complex zeros of each polynomial function f(x). ...
 5.5.1.82: In 6588: (a) Find the x and yintercepts of each polynomial funct...
 5.5.5.82: In 8188, find bounds on the real zeros of each polynomial function...
 5.83: In 8188, find the complex zeros of each polynomial function f(x). ...
 5.5.1.83: In 6588: (a) Find the x and yintercepts of each polynomial funct...
 5.5.5.83: In 8188, find bounds on the real zeros of each polynomial function...
 5.84: In 8188, find the complex zeros of each polynomial function f(x). ...
 5.5.1.84: In 6588: (a) Find the x and yintercepts of each polynomial funct...
 5.5.5.84: In 8188, find bounds on the real zeros of each polynomial function...
 5.85: In 8188, find the complex zeros of each polynomial function f(x). ...
 5.5.1.85: In 6588: (a) Find the x and yintercepts of each polynomial funct...
 5.5.5.85: In 8188, find bounds on the real zeros of each polynomial function...
 5.86: In 8188, find the complex zeros of each polynomial function f(x). ...
 5.5.1.86: In 6588: (a) Find the x and yintercepts of each polynomial funct...
 5.5.5.86: In 8188, find bounds on the real zeros of each polynomial function...
 5.87: In 8188, find the complex zeros of each polynomial function f(x). ...
 5.5.1.87: In 6588: (a) Find the x and yintercepts of each polynomial funct...
 5.5.5.87: In 8188, find bounds on the real zeros of each polynomial function...
 5.88: In 8188, find the complex zeros of each polynomial function f(x). ...
 5.5.1.88: In 6588: (a) Find the x and yintercepts of each polynomial funct...
 5.5.5.88: In 8188, find bounds on the real zeros of each polynomial function...
 5.89: Making a Can A can in the shape of a right circular cylinder is req...
 5.5.1.89: In 8998, for each polynomial function f: 73. f(x) = (x  l )(x  2...
 5.5.5.89: In 8994, use the Intermediate Value Theorem to show that each poly...
 5.5.1.90: In 8998, for each polynomial function f: 73. f(x) = (x  l )(x  2...
 5.5.5.90: In 8994, use the Intermediate Value Theorem to show that each poly...
 5.5.1.91: In 8998, for each polynomial function f: 73. f(x) = (x  l )(x  2...
 5.5.5.91: In 8994, use the Intermediate Value Theorem to show that each poly...
 5.5.1.92: In 8998, for each polynomial function f: 73. f(x) = (x  l )(x  2...
 5.5.5.92: In 8994, use the Intermediate Value Theorem to show that each poly...
 5.5.1.93: In 8998, for each polynomial function f: 73. f(x) = (x  l )(x  2...
 5.5.5.93: In 8994, use the Intermediate Value Theorem to show that each poly...
 5.5.1.94: In 8998, for each polynomial function f: 73. f(x) = (x  l )(x  2...
 5.5.5.94: In 8994, use the Intermediate Value Theorem to show that each poly...
 5.5.1.95: In 8998, for each polynomial function f: 73. f(x) = (x  l )(x  2...
 5.5.5.95: In 9598, each equation has a solution r in the interval indicated....
 5.5.1.96: In 8998, for each polynomial function f: 73. f(x) = (x  l )(x  2...
 5.5.5.96: In 9598, each equation has a solution r in the interval indicated....
 5.5.1.97: In 8998, for each polynomial function f: 73. f(x) = (x  l )(x  2...
 5.5.5.97: In 9598, each equation has a solution r in the interval indicated....
 5.5.1.98: In 8998, for each polynomial function f: 73. f(x) = (x  l )(x  2...
 5.5.5.98: In 9598, each equation has a solution r in the interval indicated....
 5.5.1.99: Hurricanes In 2005, hurricane Katrina struck the Gulf Coast of the ...
 5.5.5.99: In 99102, each polynomial function has exactly one positive zero. ...
 5.5.1.100: Active Duty The following data represent the number of active duty ...
 5.5.5.100: In 99102, each polynomial function has exactly one positive zero. ...
 5.5.1.101: Temperature The following data represent the temperature T (OFahren...
 5.5.5.101: In 99102, each polynomial function has exactly one positive zero. ...
 5.5.1.102: Can the graph of a polynomial function have no yintercept? Can it ...
 5.5.5.102: In 99102, each polynomial function has exactly one positive zero. ...
 5.5.1.103: Write a few paragraphs that provide a general strategy for graphing...
 5.5.5.103: Find k such that f(x) = x3  kx2 + kx + 2 factor x  2.
 5.5.1.104: Make up a polynomial that has the following characteristics: crosse...
 5.5.5.104: Find Ie such that f(x) = X4  kx3 + kx2 + 1 factor x + 2.
 5.5.1.105: Make up two polynomials, not of the same degree, with the following...
 5.5.5.105: What is the remainder when f(x) = 2x20  8xl0 + X  2 is divided by...
 5.5.1.106: The graph of a polynomial function is always smooth and continuous....
 5.5.5.106: What is the remainder when f(x) = 3X 1 7 + x9  XS + 2x is divided...
 5.5.1.107: Which of the following statements are true regarding the graph of t...
 5.5.5.107: Use the Factor Theorem to prove that x  c is a factor of x"  e " ...
 5.5.1.108: The illustration shows the graph of a polynomial function. (a) Is t...
 5.5.5.108: Use the Factor Theorem to prove that x + c is a factor of x" + e " ...
 5.5.1.109: Design a polynomial function with the following characteristics: de...
 5.5.5.109: One solution of the equation x3  8x2 + 16x  3 = 0 is 3. Find the ...
 5.5.5.110: One solution of the equation x3 + 5x2 + 5x  2 = 0 is 2. Find the ...
 5.5.5.111: Geometry What is the length of the edge of a cube if, after a slice...
 5.5.5.112: Geometry What is the length of the edge of a cube if its volume cou...
 5.5.5.113: Let f(x) be a polynomial function whose coefficients are integers. ...
 5.5.5.114: Prove the Rational Zeros Theorem. [Hint: Let E, where p and q have ...
 5.5.5.115: Bisection Method for Approximating Zeros of a Function f We begin w...
 5.5.5.116: Is 3" a zero of f(x) = 2x' + 3x  6x + 7? Explain.
 5.5.5.117: IS 3 " a zero of f(x) = 4x'  5x  3x + 1? Explain.
 5.5.5.118: Is a zero of f(x) = 2x6  5x4 + x3  X + I? Explain.
 5.5.5.119: Is a zero of f(x) = x 7 + 6x5  X4 + X + 2? Explain.
Solutions for Chapter 5: Polynomial and Rational Functions
Full solutions for Algebra and Trigonometry  8th Edition
ISBN: 9780132329033
Solutions for Chapter 5: Polynomial and Rational Functions
Get Full SolutionsSince 541 problems in chapter 5: Polynomial and Rational Functions have been answered, more than 86355 students have viewed full stepbystep solutions from this chapter. Algebra and Trigonometry was written by and is associated to the ISBN: 9780132329033. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 5: Polynomial and Rational Functions includes 541 full stepbystep solutions. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 8.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).