?Critical Thinking ExercisesMake Sense? In Exercises 114–117, determine whether each

Fill in each blank so that the resulting statement is true Assume that f is a function defined on an open interval I and x1 and x2 are any elements in the interval I. f is increasing on I if f(x1) _____ when x1 < x2. f is decreasing on I if f(x1) _____ when x1< x2. f is constant on I if f(x1) _____ .

Fill in each blank so that the resulting statement is true If f(a) > f(x) in an open interval containing a, \(x \neq a\) , then the function value f(a) is a relative _____ of f. If f(b) < f(x) in an open interval containing b,\(x \neq b\),then the function value f(b) is a relative _____ of f. ________________ Equation Transcription: Text Transcription: x neq a x neq b

Fill in each blank so that the resulting statement is true If f is an even function, then f(-x) = _____. Such a function is symmetric with respect to the _____ .

Fill in each blank so that the resulting statement is true If f is an odd function, then f(-x) = _____. The graph of such a function is symmetric with respect to the _____ .

Fill in each blank so that the resulting statement is true A function defined by two or more equations over a specified domain is called a/an _____ function.

Fill in each blank so that the resulting statement is true The greatest integer function is defined by int(x) = the greatest integer that is ________. For example, int(2.5) = _____ , int(-2.5) = _____, and int(0.5) = _____.

Fill in each blank so that the resulting statement is true The expression \(\frac{f(x+h)-f(x)}{h}, h \neq 0\), is called the __________ of the function f. We find this expression by replacing x with _______ each time x appears in the function’s equation. Then we subtract _______. After simplifying, we factor from the numerator and divide out identical factors _______ of in the numerator and denominator. ________________ Equation Transcription: Text Transcription: f(x+h)-f(x)/h, h neq 0

Fill in each blank so that the resulting statement is true True or false: f(x+h) = f(x) + h _____

Fill in each blank so that the resulting statement is true True or false: f(x+h) = f(x) + f(h) _____

In Exercises 1–12, use the graph to determine a. intervals on which the function is increasing, if any. b. intervals on which the function is decreasing, if any. c. intervals on which the function is constant, if any.

In Exercises 1–12, use the graph to determine a. intervals on which the function is increasing, if any. b. intervals on which the function is decreasing, if any. c. intervals on which the function is constant, if any.

In Exercises 1–12, use the graph to determine a. intervals on which the function is increasing, if any. b. intervals on which the function is decreasing, if any. c. intervals on which the function is constant, if any.

In Exercises 1–12, use the graph to determine a. intervals on which the function is increasing, if any. b. intervals on which the function is decreasing, if any. c. intervals on which the function is constant, if any.

In Exercises 1–12, use the graph to determine a. intervals on which the function is increasing, if any. b. intervals on which the function is decreasing, if any. c. intervals on which the function is constant, if any.

In Exercises 1–12, use the graph to determine a. intervals on which the function is increasing, if any. b. intervals on which the function is decreasing, if any. c. intervals on which the function is constant, if any.

In Exercises 1–12, use the graph to determine a. intervals on which the function is increasing, if any. b. intervals on which the function is decreasing, if any. c. intervals on which the function is constant, if any.

In Exercises 1–12, use the graph to determine a. intervals on which the function is increasing, if any. b. intervals on which the function is decreasing, if any. c. intervals on which the function is constant, if any.

In Exercises 1–12, use the graph to determine a. intervals on which the function is increasing, if any. b. intervals on which the function is decreasing, if any. c. intervals on which the function is constant, if any.

In Exercises 1–12, use the graph to determine a. intervals on which the function is increasing, if any. b. intervals on which the function is decreasing, if any. c. intervals on which the function is constant, if any.

In Exercises 1–12, use the graph to determine a. intervals on which the function is increasing, if any. b. intervals on which the function is decreasing, if any. c. intervals on which the function is constant, if any.

In Exercises 1–12, use the graph to determine a. intervals on which the function is increasing, if any. b. intervals on which the function is decreasing, if any. c. intervals on which the function is constant, if any.

In Exercises 13–16, the graph of a function f is given. Use the graph to find each of the following: a. The numbers, if any, at which f has a relative maximum. What are these relative maxima? b. The numbers, if any, at which f has a relative minimum. What are these relative minima?

In Exercises 13–16, the graph of a function f is given. Use the graph to find each of the following: a. The numbers, if any, at which f has a relative maximum. What are these relative maxima? b. The numbers, if any, at which f has a relative minimum. What are these relative minima?

In Exercises 13–16, the graph of a function f is given. Use the graph to find each of the following: a. The numbers, if any, at which f has a relative maximum. What are these relative maxima? b. The numbers, if any, at which f has a relative minimum. What are these relative minima?

In Exercises 13–16, the graph of a function f is given. Use the graph to find each of the following: a. The numbers, if any, at which f has a relative maximum. What are these relative maxima? b. The numbers, if any, at which f has a relative minimum. What are these relative minima?

In Exercises 17–28, determine whether each function is even, odd, or neither. \(f(x)=x^{3}+x\) ________________ Equation Transcription: Text Transcription: f(x)=x^3+x

In Exercises 17–28, determine whether each function is even, odd, or neither. \(f(x)=x^{3}-x\) ________________ Equation Transcription: Text Transcription: f(x)=x^3-x

In Exercises 17–28, determine whether each function is even, odd, or neither. \(g(x)=x^{2}+x\) ________________ Equation Transcription: Text Transcription: g(x)=x^2+x

In Exercises 17–28, determine whether each function is even, odd, or neither. \(g(x)=x^{2}-x\) ________________ Equation Transcription: Text Transcription: g(x)=x^2-x

In Exercises 17–28, determine whether each function is even, odd, or neither. \(h(x)=x^{2}-x^{4}\) ________________ Equation Transcription: Text Transcription: h(x)=x^2-x^4

In Exercises 17–28, determine whether each function is even, odd, or neither. \(h(x)=2 x^{2}+x^{4}\) ________________ Equation Transcription: Text Transcription: h(x)=2x^2+x^4

In Exercises 17–28, determine whether each function is even, odd, or neither. \(f(x)=x^{2}-x^{4}+1\) ________________ Equation Transcription: Text Transcription: f(x)=x^2-x^4+1

In Exercises 17–28, determine whether each function is even, odd, or neither. \(f(x)=2 x^{2}+x^{4}+1\) ________________ Equation Transcription: Text Transcription: f(x)=2x^2+x^4+1

In Exercises 17–28, determine whether each function is even, odd, or neither. \(f(x)=\frac{1}{5} x^{6}-3 x^{2}\) ________________ Equation Transcription: Text Transcription: f(x)=1/5x^6-3x^2

In Exercises 17–28, determine whether each function is even, odd, or neither. \(f(x)=2 x^{3}-6 x^{5}\) ________________ Equation Transcription: Text Transcription: f(x)=2x^3-6x^5

In Exercises 17–28, determine whether each function is even, odd, or neither. \(f(x)=x \sqrt{1-x^{2}}\) ________________ Equation Transcription: Text Transcription: f(x)=x sqrt 1 - x^2

In Exercises 17–28, determine whether each function is even, odd, or neither. \(f(x)=x^{2} \sqrt{1-x^{2}}\) ________________ Equation Transcription: Text Transcription: f(x)=x^2 sqrt 1-x^2

In Exercises 29–32, use possible symmetry to determine whether each graph is the graph of an even function, an odd function, or a function that is neither even nor odd.

In Exercises 29–32, use possible symmetry to determine whether each graph is the graph of an even function, an odd function, or a function that is neither even nor odd.

In Exercises 29–32, use possible symmetry to determine whether each graph is the graph of an even function, an odd function, or a function that is neither even nor odd.

In Exercises 29–32, use possible symmetry to determine whether each graph is the graph of an even function, an odd function, or a function that is neither even nor odd.

Use the graph of f to determine each of the following. Where applicable, use interval notation. a. the domain of f b. the range of f c. the x-intercepts d. the y-intercept e. intervals on which f is increasing f. intervals on which f is decreasing g. intervals on which f is constant h. the number at which f has a relative minimum i. the relative minimum of f j. \(f(-3) \) k. the values of x for which \(f(x)=-2 \) l. Is f even, odd, or neither? ________________ Equation Transcription: Text Transcription: f(-3) f(x)=-2

Use the graph of f to determine each of the following. Where applicable, use interval notation. a. the domain of f b. the range of f c. the x-intercepts d. the y-intercept e. intervals on which f is increasing f. intervals on which f is decreasing g. values of x for which \(f(x) \leq 0\) h. the numbers at which f has a relative maximum i. the relative maxima of f j. \(f(-2)\) k. the values of x for which \(f(x)=0\) l. Is f even, odd, or neither? ________________ Equation Transcription: Text Transcription: f(x) leq 0 f(-2) f(x)=0

Use the graph of f to determine each of the following. Where applicable, use interval notation. a. the domain of f b. the range of f c. the zeros of f d. \(f(0)\) e. intervals on which f is increasing f. intervals on which f is decreasing g. values of x for which \(f(x) \leq 0\) h. any relative maxima and the numbers at which they occur i. the value of x for which \(f(x)=4\) j. Is \(f(-1)\) positive or negative? ________________ Equation Transcription: Text Transcription: f(0) f(x) leq 0 f(x)=4 f(-1)

Use the graph of f to determine each of the following. Where applicable, use interval notation. a. the domain of f b. the range of f c. the zeros of f d. \(f(0)\) e. intervals on which f is increasing f. intervals on which f is decreasing g. intervals on which f is constant h. values of x for which \(f(x)>0\) i. values of x for which \(f(x)=-2\) j. Is \(f(4)\) positive or negative? k. Is f even, odd, or neither? l. Is \(f(2)\) a relative maximum? ________________ Equation Transcription: Text Transcription: f(0) f(x) > 0 f(x)=-2 f(4) f(2)

In Exercises 37–42, evaluate each piecewise function at the given values of the independent variable. \(f(x)=\left\{\begin{array}{lll} 3 x+5 & \text { if } & x<0 \\ 4 x+7 & \text { if } & x \geq 0 \end{array}\right. \) a. f(-2) b. f(0) c. f(3) ________________ Equation Transcription: { Text Transcription: f(x)={3x+5 if x < 0 4x+7 if x geq 0

In Exercises 37–42, evaluate each piecewise function at the given values of the independent variable. \(f(x)=\left\{\begin{array}{lll} 6 x-1 & \text { if } & x<0 \\ 7 x+3 & \text { if } & x \geq 0 \end{array}\right. \) a. f(-3) b. f(0) c. f(4) ________________ Equation Transcription: { Text Transcription: f(x)={6x-1 if x < 0 7x+3 if x geq 0

In Exercises 37–42, evaluate each piecewise function at the given values of the independent variable. \(g(x)=\left\{\begin{array}{lll} x+3 & \text { if } & x \geq-3 \\ -(x+3) & \text { if } & x<-3 \end{array}\right. \) a. g(0) b. g(-6) c. g(-3) ________________ Equation Transcription: { Text Transcription: g(x)={x+3 if x geq -3 -(x+3) if x < -3

In Exercises 37–42, evaluate each piecewise function at the given values of the independent variable. \(g(x)=\left\{\begin{array}{lll} x+5 & \text { if } & x \geq-5 \\ -(x+5) & \text { if } & x<-5 \end{array}\right. \) a. g(0) b. g(-6) c. g(-5) ________________ Equation Transcription: { Text Transcription: g(x)={x+5 if x geq -5 -(x+5) if x < -5

In Exercises 37–42, evaluate each piecewise function at the given values of the independent variable. \(h(x)=\left\{\begin{array}{lll} \frac{x^{2}-9}{x-3} & \text { if } & x \neq 3 \\ 6 & \text { if } & x=3 \end{array}\right. \) a. h(5) b. h(0) c. h(3) ________________ Equation Transcription: { Text Transcription: h(x)={x^2-9/x-3 if x neq 3 6 if x=3

In Exercises 37–42, evaluate each piecewise function at the given values of the independent variable. \(h(x)=\left\{\begin{array}{lll} \frac{x^{2}-25}{x-5} & \text { if } & x \neq 5 \\ 10 & \text { if } & x=5 \end{array}\right. \) a. h(7) b. h(0) c. h(5) ________________ Equation Transcription: { Text Transcription: h(x)={x^2-25/x-5 if x neq 5 10 if x=5

In Exercises 43–54, the domain of each piecewise function is (\(-\infty, \infty\)). a. Graph each function. b. Use your graph to determine the function’s range. \(f(x)=\left\{\begin{array}{lll} -x & \text { if } & x<2 \\ x & \text { if } & x \geq 0 \end{array}\right. \) ________________ Equation Transcription: , { Text Transcription: -infinity, infinity f(x)={-x if x < 2 x if x geq 0

In Exercises 43–54, the domain of each piecewise function is (\(-\infty, \infty\)). a. Graph each function. b. Use your graph to determine the function’s range. \(f(x)=\left\{\begin{array}{lll} x & \text { if } & x<2 \\ -x & \text { if } & x \geq 0 \end{array}\right. \) ________________ Equation Transcription: , { Text Transcription: -infinity, infinity f(x)={x if x < 2 -x if x geq 0

In Exercises 43–54, the domain of each piecewise function is (\(-\infty, \infty\)). a. Graph each function. b. Use your graph to determine the function’s range. \(f(x)=\left\{\begin{array}{lll} 2 x & \text { if } & x \leq 2 \\ 2 & \text { if } & x>0 \end{array}\right. \) ________________ Equation Transcription: , { Text Transcription: -infinity, infinity f(x)={2x if x leq 2 2 if x > 0

In Exercises 43–54, the domain of each piecewise function is (\(-\infty, \infty\)). a. Graph each function. b. Use your graph to determine the function’s range. \(f(x)=\left\{\begin{array}{lll} \frac{1}{2} x & \text { if } & x \leq 2 \\ 3 & \text { if } & x>0 \end{array}\right. \) ________________ Equation Transcription: , { Text Transcription: -infinity, infinity f(x)={1/2x if x leq 2 3 if x > 0

In Exercises 43–54, the domain of each piecewise function is (\(-\infty, \infty\)). a. Graph each function. b. Use your graph to determine the function’s range. \(f(x)=\left\{\begin{array}{lll} x+3 & \text { if } & x<-2 \\ x-3 & \text { if } & x \geq-2 \end{array}\right. \) ________________ Equation Transcription: , { Text Transcription: -infinity, infinity f(x)={x+3 if x < -2 x-3 if x geq -2

In Exercises 43–54, the domain of each piecewise function is (\(-\infty, \infty\)). a. Graph each function. b. Use your graph to determine the function’s range. \(f(x)=\left\{\begin{array}{lll} x+2 & \text { if } & x<-3 \\ x-2 & \text { if } & x \geq-3 \end{array}\right. \) ________________ Equation Transcription: , { Text Transcription: -infinity, infinity f(x)={x+2 if x < -4 x-2 if x geq -3

In Exercises 43–54, the domain of each piecewise function is (\(-\infty, \infty\)). a. Graph each function. b. Use your graph to determine the function’s range. \(f(x)=\left\{\begin{array}{lll} 3 & \text { if } & x \leq-1 \\ -3 & \text { if } & x>-1 \end{array}\right. \) ________________ Equation Transcription: , { Text Transcription: -infinity, infinity f(x)={3 if x leq -1 -3 if x > -1

In Exercises 43–54, the domain of each piecewise function is (\(-\infty, \infty\)). a. Graph each function. b. Use your graph to determine the function’s range. \(f(x)=\left\{\begin{array}{lll} 4 & \text { if } & x \leq-1 \\ -4 & \text { if } & x>-1 \end{array}\right. \) ________________ Equation Transcription: , { Text Transcription: -infinity, infinity f(x)={4 if x leq -1 -4 if x > -1

In Exercises 43–54, the domain of each piecewise function is (\(-\infty, \infty\)). a. Graph each function. b. Use your graph to determine the function’s range. \(f(x)=\left\{\begin{array}{lll} \frac{1}{2} x^{2} & \text { if } & x<1 \\ 2 x-1 & \text { if } & x \geq 1 \end{array}\right. \) ________________ Equation Transcription: , { Text Transcription: -infinity, infinity f(x)={1/2x^2 if x<1 2x-1 if x geq 1

In Exercises 43–54, the domain of each piecewise function is (\(-\infty, \infty\)). a. Graph each function. b. Use your graph to determine the function’s range. \(f(x)=\left\{\begin{array}{ccc} -\frac{1}{2} x^{2} & \text { if } & x<1 \\ 2 x+1 & \text { if } & x \geq 1 \end{array}\right. \) ________________ Equation Transcription: , { Text Transcription: -infinity, infinity f(x)={-1/2x^2 if x<1 2x+1 if x geq 1

In Exercises 43–54, the domain of each piecewise function is (\(-\infty, \infty\)). a. Graph each function. b. Use your graph to determine the function’s range. \(f(x)=\left\{\begin{array}{lll} 0 & \text { if } & x<-4 \\ -x & \text { if } & -4 \leq x<0 \\ x^{2} & \text { if } & x \geq 0 \end{array}\right. \) ________________ Equation Transcription: , { Text Transcription: -infinity, infinity f(x)={0 if x < -4 -x if -4 leq x < 0 x^2 if x geq 0

In Exercises 43–54, the domain of each piecewise function is (\(-\infty, \infty\)). a. Graph each function. b. Use your graph to determine the function’s range. \(f(x)=\left\{\begin{array}{ccc} 0 & \text { if } & x<-3 \\ -x & \text { if } & -3 \leq x<0 \\ x^{2}-1 & \text { if } & x \geq 0 \end{array}\right. \) ________________ Equation Transcription: , { Text Transcription: -infinity, infinity f(x)={0 if x < -3 -x if -3 leq x < 0 x^2-1 if x geq 0

In Exercises 55–76, find and simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}, h \neq 0\) for the given function. \(f(x)=4 x\) ________________ Equation Transcription: Text Transcription: f(x+h)-f(x)/h, h neq 0 f(x)=4x

In Exercises 55–76, find and simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}, h \neq 0\) for the given function. \(f(x)=7x\) ________________ Equation Transcription: Text Transcription: f(x+h)-f(x)/h, h neq 0 f(x)=7x

In Exercises 55–76, find and simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}, h \neq 0\) for the given function. \(f(x)=3x+7\) ________________ Equation Transcription: Text Transcription: f(x+h)-f(x)/h, h neq 0 f(x)=3x+7

In Exercises 55–76, find and simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}, h \neq 0\) for the given function. \(f(x)=6x+1\) ________________ Equation Transcription: Text Transcription: f(x+h)-f(x)/h, h neq 0 f(x)=6x+1

In Exercises 55–76, find and simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}, h \neq 0\) for the given function. \(f(x)=x^{2}\) ________________ Equation Transcription: Text Transcription: f(x+h)-f(x)/h, h neq 0 f(x)=x^2

In Exercises 55–76, find and simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}, h \neq 0\) for the given function. \(f(x)=2 x^{2}\) ________________ Equation Transcription: Text Transcription: f(x+h)-f(x)/h, h neq 0 f(x)=2x^2

In Exercises 55–76, find and simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}, h \neq 0\) for the given function. \(f(x)=x^{2}-4 x+3\) ________________ Equation Transcription: Text Transcription: f(x+h)-f(x)/h, h neq 0 f(x)=x^2-4x+3

In Exercises 55–76, find and simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}, h \neq 0\) for the given function. \(f(x)=x^{2}-5 x+8\) ________________ Equation Transcription: Text Transcription: f(x+h)-f(x)/h, h neq 0 f(x)=x^2-5x+8

In Exercises 55–76, find and simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}, h \neq 0\) for the given function. \(f(x)=2 x^{2}+x-1\) ________________ Equation Transcription: Text Transcription: f(x+h)-f(x)/h, h neq 0 f(x)=2x^2+x-1

In Exercises 55–76, find and simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}, h \neq 0\) for the given function. \(f(x)=3 x^{2}+x+5\) ________________ Equation Transcription: Text Transcription: f(x+h)-f(x)/h, h neq 0 f(x)=3x^2+x+5

In Exercises 55–76, find and simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}, h \neq 0\) for the given function. \(f(x)=-x^{2}+2 x+4\) ________________ Equation Transcription: Text Transcription: f(x+h)-f(x)/h, h neq 0 f(x)=-x^2+2x+4

In Exercises 55–76, find and simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}, h \neq 0\) for the given function. \(f(x)=-x^{2}-3 x+1\) ________________ Equation Transcription: Text Transcription: f(x+h)-f(x)/h, h neq 0 f(x)=-x^2-3x+1

In Exercises 55–76, find and simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}, h \neq 0\) for the given function. \(f(x)=-2 x^{2}+5 x+7\) ________________ Equation Transcription: Text Transcription: f(x+h)-f(x)/h, h neq 0 f(x)=-2x^2+5x+7

In Exercises 55–76, find and simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}, h \neq 0\) for the given function. \(f(x)=-3 x^{2}+2 x-1\) ________________ Equation Transcription: Text Transcription: f(x+h)-f(x)/h, h neq 0 f(x)=-3x^2+2x-1

In Exercises 55–76, find and simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}, h \neq 0\) for the given function. \(f(x)=-2 x^{2}-x+3\) ________________ Equation Transcription: Text Transcription: f(x+h)-f(x)/h, h neq 0 f(x)=-2x^2-x+3

In Exercises 55–76, find and simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}, h \neq 0\) for the given function. \(f(x)=-3 x^{2}+x-1\) ________________ Equation Transcription: Text Transcription: f(x+h)-f(x)/h, h neq 0 f(x)=-3x^2+x-1

In Exercises 55–76, find and simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}, h \neq 0\) for the given function. \(f(x)=6\) ________________ Equation Transcription: Text Transcription: f(x+h)-f(x)/h, h neq 0 f(x)=6

In Exercises 55–76, find and simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}, h \neq 0\) for the given function. \(f(x)=7\) ________________ Equation Transcription: Text Transcription: f(x+h)-f(x)/h, h neq 0 f(x)=7

In Exercises 55–76, find and simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}, h \neq 0\) for the given function. \(f(x)=\frac{1}{x}\) ________________ Equation Transcription: Text Transcription: f(x+h)-f(x)/h, h neq 0 f(x)=1/x

In Exercises 55–76, find and simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}, h \neq 0\) for the given function. \(f(x)=\frac{1}{2 x}\) ________________ Equation Transcription: Text Transcription: f(x+h)-f(x)/h, h neq 0 f(x)=1/2x

In Exercises 55–76, find and simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}, h \neq 0\) for the given function. \(f(x)=\sqrt{x}\) ________________ Equation Transcription: Text Transcription: f(x+h)-f(x)/h, h neq 0 f(x)=sqrt x

In Exercises 55–76, find and simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}, h \neq 0\) for the given function. \(f(x)=\sqrt{x-1}\) ________________ Equation Transcription: Text Transcription: f(x+h)-f(x)/h, h neq 0 f(x)=sqrt x-1

In Exercises 77–78, let f be defined by the following graph: \(\sqrt{f(-1.5)+f(-0.9)}-[f(\pi)]^{2}+f(-3) \div f(1) \cdot f(-\pi)\) ________________ Equation Transcription: Text Transcription: Sqrt f(-1.5)+f(-0.9)-[f(pi)]^2+f(-3) div f(1) times f(-pi)

In Exercises 77–78, let f be defined by the following graph: \(\sqrt{f(-2.5)+f(1.9)}-[f(-\pi)]^{2}+f(-3) \div f(1) \cdot f(\pi)\) ________________ Equation Transcription: Text Transcription: Sqrt f(-2.5)+f(1.9)-[f(-pi)]^2+f(-3) div f(1) times f(pi)

A cellphone company offers the following plans. Also given are the piecewise functions that model these plans. Use this information to solve Exercises 79–80. Plan A • $30 per month buys 120 minutes. • Additional time costs $0.30 per minute. \(C(t)=\left\{\begin{array}{lll} 30 & \text { if } & 0 \leq t \leq 120 \\ 30+0.30(t-120) & \text { if } & t>120 \end{array}\right. \) Plan B • $40 per month buys 200 minutes. • Additional time costs $0.30 per minute. \(C(t)=\left\{\begin{array}{lll} 40 & \text { if } & 0 \leq t \leq 200 \\ 40+0.30(t-120) & \text { if } & t>200 \end{array}\right. \) Simplify the algebraic expression in the second line of the piecewise function for plan A. Then use point-plotting to graph the function. ________________ Equation Transcription: { { Text Transcription: C(t) = { 30 if 0 leq t leq 120 30 + 0.30(t-120 if t > 120) C(t) = { 40 if 0 leq t leq 200 40 + 0.30(t-120 if t > 200)

A cellphone company offers the following plans. Also given are the piecewise functions that model these plans. Use this information to solve Exercises 79–80. Plan A • $30 per month buys 120 minutes. • Additional time costs $0.30 per minute. \(C(t)=\left\{\begin{array}{lll} 30 & \text { if } & 0 \leq t \leq 120 \\ 30+0.30(t-120) & \text { if } & t>120 \end{array}\right. \) Plan B • $40 per month buys 200 minutes. • Additional time costs $0.30 per minute. \(C(t)=\left\{\begin{array}{lll} 40 & \text { if } & 0 \leq t \leq 200 \\ 40+0.30(t-120) & \text { if } & t>200 \end{array}\right. \) Simplify the algebraic expression in the second line of the piecewise function for plan B. Then use point-plotting to graph the function. ________________ Equation Transcription: { { Text Transcription: C(t) = { 30 if 0 leq t leq 120 30 + 0.30(t-120 if t > 120) C(t) = { 40 if 0 leq t leq 200 40 + 0.30(t-120 if t > 200)

In Exercises 81–82, write a piecewise function that models each cellphone billing plan. Then graph the function. $50 per month buys 400 minutes. Additional time costs $0.30 per minute.

In Exercises 81–82, write a piecewise function that models each cellphone billing plan. Then graph the function. $60 per month buys 450 minutes. Additional time costs $0.35 per minute.

Application Exercises With aging, body fat increases and muscle mass declines. The line graphs show the percent body fat in adult women and men as they age from 25 to 75 years. Use the graphs to solve Exercises 83–90. State the intervals on which the graph giving the percent body fat in women is increasing and decreasing.

Application Exercises With aging, body fat increases and muscle mass declines. The line graphs show the percent body fat in adult women and men as they age from 25 to 75 years. Use the graphs to solve Exercises 83–90. State the intervals on which the graph giving the percent body fat in men is increasing and decreasing.

Application Exercises With aging, body fat increases and muscle mass declines. The line graphs show the percent body fat in adult women and men as they age from 25 to 75 years. Use the graphs to solve Exercises 83–90. For what age does the percent body fat in women reach a maximum? What is the percent body fat for that age?

Application Exercises With aging, body fat increases and muscle mass declines. The line graphs show the percent body fat in adult women and men as they age from 25 to 75 years. Use the graphs to solve Exercises 83–90. At what age does the percent body fat in men reach a maximum? What is the percent body fat for that age?

Application Exercises With aging, body fat increases and muscle mass declines. The line graphs show the percent body fat in adult women and men as they age from 25 to 75 years. Use the graphs to solve Exercises 83–90. Use interval notation to give the domain and the range for the graph of the function for women.

Application Exercises With aging, body fat increases and muscle mass declines. The line graphs show the percent body fat in adult women and men as they age from 25 to 75 years. Use the graphs to solve Exercises 83–90. Use interval notation to give the domain and the range for the graph of the function for men.

Application Exercises With aging, body fat increases and muscle mass declines. The line graphs show the percent body fat in adult women and men as they age from 25 to 75 years. Use the graphs to solve Exercises 83–90. The function \(p(x)=-0.002 x^{2}+0.15 x+22.86\) models percent body fat, p(x), where x is the number of years a person’s age exceeds 25. Use the graphs to determine whether this model describes percent body fat in women or in men. ________________ Equation Transcription: Text Transcription: p(x)=-0.002x^2+0.15x+22.86

Application Exercises With aging, body fat increases and muscle mass declines. The line graphs show the percent body fat in adult women and men as they age from 25 to 75 years. Use the graphs to solve Exercises 83–90. The function \(p(x)=-0.004 x^{2}+0.25 x+33.64\) models percent body fat, p(x), where x is the number of years a person’s age exceeds 25. Use the graphs to determine whether this model describes percent body fat in women or in men. ________________ Equation Transcription: Text Transcription: p(x)=-0.004x^2+0.25x+33.64

Here is the 2011 Federal Tax Rate Schedule X that specifies the tax owed by a single taxpayer. The preceding tax table can be modeled by a piecewise function, where x represents the taxable income of a single taxpayer and T(x) is the tax owed: Use this information to solve Exercises 91–94. Find and interpret T(20,000).

Here is the 2011 Federal Tax Rate Schedule X that specifies the tax owed by a single taxpayer. The preceding tax table can be modeled by a piecewise function, where x represents the taxable income of a single taxpayer and T(x) is the tax owed: Use this information to solve Exercises 91–94. Find and interpret T(50,000).

Here is the 2011 Federal Tax Rate Schedule X that specifies the tax owed by a single taxpayer. The preceding tax table can be modeled by a piecewise function, where x represents the taxable income of a single taxpayer and T(x) is the tax owed: Use this information to solve Exercises 91–94. In Exercises 93–94, refer to the preceding tax table. Find the algebraic expression for the missing piece of T(x)that models tax owed for the domain (174,400, 379,150].

Here is the 2011 Federal Tax Rate Schedule X that specifies the tax owed by a single taxpayer. The preceding tax table can be modeled by a piecewise function, where x represents the taxable income of a single taxpayer and T(x) is the tax owed: Use this information to solve Exercises 91–94. In Exercises 93–94, refer to the preceding tax table. Find the algebraic expression for the missing piece of T(x)that models tax owed for the domain (379,150, \(\infty\)). ________________ Equation Transcription: Text Transcription: infinity

The figure shows the cost of mailing a first-class letter, f(x), as a function of its weight, x, in ounces. Use the graph to solve Exercises 95–98. Find f(3). What does this mean in terms of the variables in this situation?

The figure shows the cost of mailing a first-class letter, f(x), as a function of its weight, x, in ounces. Use the graph to solve Exercises 95–98. Find f(3.5). What does this mean in terms of the variables in this situation?

The figure shows the cost of mailing a first-class letter, f(x), as a function of its weight, x, in ounces. Use the graph to solve Exercises 95–98. What is the cost of mailing a letter that weighs 1.5 ounces?

The figure shows the cost of mailing a first-class letter, f(x), as a function of its weight, x, in ounces. Use the graph to solve Exercises 95–98. What is the cost of mailing a letter that weighs 1.8 ounces?

The figure shows the cost of mailing a first-class letter, f(x), as a function of its weight, x, in ounces. Use the graph to solve Exercises 95–98. Furry Finances A pet insurance policy has a monthly rate that is a function of the age of the insured dog or cat. For pets whose age does not exceed 4, the monthly cost is $20. The cost then increases by $2 for each successive year of the pet’s age The cost schedule continues in this manner for ages not exceeding 10. The cost for pets whose ages exceed 10 is $40. Use this information to create a graph that shows the monthly cost of the insurance, f(x), for a pet of age x, where the function’s domain is [0, 14].

Writing in Mathematics What does it mean if a function f is increasing on an interval?

Writing in Mathematics Suppose that a function f whose graph contains no breaks or gaps on (a,c) is increasing on (a,b), decreasing on (b,c), and defined at b. Describe what occurs at x=b. What does the function valuef(b) represent?

Writing in Mathematics If you are given a function’s equation, how do you determine if the function is even, odd, or neither?

Writing in Mathematics If you are given a function’s graph, how do you determine if the function is even, odd, or neither?

Writing in Mathematics What is a piecewise function?

Writing in Mathematics Explain how to find the difference quotient of a function f , \(\frac{f(x+h)-f(x)}{h}\), if an equation for f is given. ________________ Equation Transcription: Text Transcription: f(x+h)-f(x)/h

Technology Exercises \(f(x)=-0.00002 x^{3}+0.008 x^{2}-0.3 x+6.95\) models the number of annual physician visits, f(x), by a person of age x. Graph the function in a [0, 100, 5] by [0, 40, 2] viewing rectangle. What does the shape of the graph indicate about the relationship between one’s age and the number of annual physician visits? Use the TABLEor minimum function capability to find the coordinates of the minimum point on the graph of the function. What does this mean? ________________ Equation Transcription: Text Transcription: f(x)=-0.00002x^3+0.008x^2-0.3x+6.95

In Exercises 107–112, use a graphing utility to graph each function. Use a [-5, 5, 1] by [-5, 5, 1] viewing rectangle. Then find the intervals on which the function is increasing, decreasing, or constant. \(f(x)=x^{3}-6 x^{2}+9 x+1\) ________________ Equation Transcription: Text Transcription: f(x)=x^3-6x^2+9x+1

In Exercises 107–112, use a graphing utility to graph each function. Use a [-5, 5, 1] by [-5, 5, 1] viewing rectangle. Then find the intervals on which the function is increasing, decreasing, or constant. \(g(x)=\left|4-x^{2}\right|\) ________________ Equation Transcription: Text Transcription: g(x)=|4-x^2|

In Exercises 107–112, use a graphing utility to graph each function. Use a [-5, 5, 1] by [-5, 5, 1] viewing rectangle. Then find the intervals on which the function is increasing, decreasing, or constant. \(h(x)=|x-2|+|x+2|\) ________________ Equation Transcription: Text Transcription: h(x)=|x-2|+|x+2|

In Exercises 107–112, use a graphing utility to graph each function. Use a [-5, 5, 1] by [-5, 5, 1] viewing rectangle. Then find the intervals on which the function is increasing, decreasing, or constant. \(f(x)=x^{\frac{1}{3}}(x-4)\) ________________ Equation Transcription: Text Transcription: f(x)=x^1/3(x-4)

In Exercises 107–112, use a graphing utility to graph each function. Use a [-5, 5, 1] by [-5, 5, 1] viewing rectangle. Then find the intervals on which the function is increasing, decreasing, or constant. \(g(x)=x^{\frac{2}{3}}\) ________________ Equation Transcription: Text Transcription: g(x)=x^2/3

In Exercises 107–112, use a graphing utility to graph each function. Use a [-5, 5, 1] by [-5, 5, 1] viewing rectangle. Then find the intervals on which the function is increasing, decreasing, or constant. \(h(x)=2-x^{\frac{2}{5}}\) ________________ Equation Transcription: Text Transcription: h(x)=2-x^2/5

a. Graph the functions \(f(x)=x^{n} \text { for } n=2,4, \text { and } 6 \text { in } a[-2,2,1] \text { by }[-1,3,1]\) viewing rectangle. b. Graph the functions \(f(x)=x^{n} \text { for } n=1,3, \text { and } 5 \text { in } a[-2,2,1] \text { by }[-2,2,1]\) viewing rectangle. c. If n is positive and even, where is the graph of \(f(x)=x^{n}\) increasing and where is it decreasing? d. If n is positive and odd, what can you conclude about the graph of \(f(x)=x^{n}\) in terms of increasing or decreasing behavior? e. Graph all six functions in a \([-1,3,1] \text { by }[-1,3,1]\) viewing rectangle. What do you observe about the graphs in terms of how flat or how steep they are? ________________ Equation Transcription: Text Transcription: f(x) = x^n for n = 2, 4 , and 6 in a [-2, 2, 1] by [-1, 3, 1] f(x) = x^n for n = 1, 3, and 5 in a [-2, 2, 1] by [-2, 2, 1] f(x) = x^n [ -1, 3, 1] by [-1, 3, 1]

Critical Thinking Exercises Make Sense? In Exercises 114–117, determine whether each statement makes sense or does not make sense, and explain your reasoning. My graph is decreasing on \((-\infty, a)\) and increasing on \((a, \infty)\), so f(a) must be a relative maximum. ________________ Equation Transcription: Text Transcription: (-infinity, a) (a, infinity)

Critical Thinking Exercises Make Sense? In Exercises 114–117, determine whether each statement makes sense or does not make sense, and explain your reasoning. This work by artist Scott Kim (1955–) has the same kind of symmetry as an even function.

Critical Thinking Exercises Make Sense? In Exercises 114–117, determine whether each statement makes sense or does not make sense, and explain your reasoning. I graphed \(f(x)=\left\{\begin{array}{lll} 2 & \text { if } & x \neq 2 \\ 3 & \text { if } & x=4 \end{array}\right. \) and one piece of my graph is a single point. ________________ Equation Transcription: { Text Transcription: f(x)={2 if x neq 2 3 if x = 4

Critical Thinking Exercises Make Sense? In Exercises 114–117, determine whether each statement makes sense or does not make sense, and explain your reasoning. I noticed that the difference quotient is always zero if \(f(x)=c\), where c is any constant. ________________ Equation Transcription: Text Transcription: f(x)=c

Sketch the graph of f using the following properties. (More than one correct graph is possible.) f is a piecewise function that is decreasing on (\(-\infty\), 2), f(2) = 0, f is increasing on ( 2, \(\infty\)), and the range of f i s [ 0, \(\infty\)). ________________ Equation Transcription: Text Transcription: -infinity infinity

Define a piecewise function on the intervals (\(-\infty\), 2], (2, 5), and [5, \(\infty\)) that does not “jump” at 2 or 5 such that one piece is a constant function, another piece is an increasing function, and the third piece is a decreasing function. ________________ Equation Transcription: Text Transcription: -infinity infinity

Suppose that \(h(x)=\frac{f(x)}{g(x)}\). The function f can be even, odd, or neither. The same is true for the function g. a. Under what conditions is he definitely an even function? b. Under what conditions is function? ________________ Equation Transcription: Text Transcription: h(x)=f(x)/g(x)

Group Exercise (For assistance with this exercise, refer to the discussion of piecewise functions beginning on page 234, as well as to Exercises 79–80.) Group members who have cellphone plans should describe the total monthly cost of the plan as follows: $_____ per month buys _____ minutes. Additional time costs $_____ per minute. (For simplicity, ignore other charges.) The group should select any three plans, from “basic” to “premier.” For each plan selected, write a piecewise function that describes the plan and graph the function. Graph the three functions in the same rectangular coordinate system. Now examine the graphs. For any given number of calling minutes, the best plan is the one whose graph is lowest at that point. Compare the three calling plans. Is one plan always a better deal than the other two? If not, determine the interval of calling minutes for which each plan is the best deal. (You can check out cellphone plans by visiting www.point.com .)

Exercises 122–124 will help you prepare for the material covered in the next section. If \(\left(x_{1}, y_{1}\right)=(-3,1) \text { and }\left(x_{2}, y_{2}\right)=(-2,4) \text {. find } \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\). ________________ Equation Transcription: Text Transcription: (x_1,y_1)=(-3, 1) and (x_2,y_2)=(-2,4). find y_2-y_1/x_2-x_1

Exercises 122–124 will help you prepare for the material covered in the next section. Find the ordered pairs (____, 0) and (0, _____) satisfying \(4x-3y-6=0\). ________________ Equation Transcription: Text Transcription: 4x-3y-6=0

Exercises 122–124 will help you prepare for the material covered in the next section. Solve for \(y:3x+2y-4=0\). ________________ Equation Transcription: Text Transcription: y:3x+2y-4=0