 2.1: In Exercises 12, evaluate the function for x = 7.f(x) = x/2 1
 2.2: In Exercises 12, evaluate the function for x = 7.f(x) = x2 3
 2.3: For Exercises 36, calculate exactly the values of y when y = f(4) a...
 2.4: For Exercises 36, calculate exactly the values of y when y = f(4) a...
 2.5: For Exercises 36, calculate exactly the values of y when y = f(4) a...
 2.6: For Exercises 36, calculate exactly the values of y when y = f(4) a...
 2.7: If f(x)=2x + 1, (a) Find f(0) (b) Solve f(x)=0.
 2.8: If f(x) = x 1 x2 , find f(2).
 2.9: If P(t) = 170 4t, find P(4) P(2).
 2.10: Let h(x)=1/x. Find (a) h(x + 3) (b) h(x) + h(3)
 2.11: (a) Using Table 2.20, evaluate f(1), f(1), and f(1). (b) Solve f(x)...
 2.12: (a) In Figure 2.29, estimate f(0). (b) For what xvalue(s) is f(x)=...
 2.13: Find the domain and range of functions in Exercises 1318 algebraica...
 2.14: Find the domain and range of functions in Exercises 1318 algebraica...
 2.15: Find the domain and range of functions in Exercises 1318 algebraica...
 2.16: Find the domain and range of functions in Exercises 1318 algebraica...
 2.17: Find the domain and range of functions in Exercises 1318 algebraica...
 2.18: Find the domain and range of functions in Exercises 1318 algebraica...
 2.19: (a) How can you tell from the graph of a function that an xvalue i...
 2.20: Let g(x) = x2 + x. Evaluate and simplify the following. (a) 3g(x) (...
 2.21: Let f(x)=1 x. Evaluate and simplify the following. (a) 2f(x) (b) f(...
 2.22: In Exercises 2223, let f(x)=3x 7 and g(x) = x3 + 1 to find a formul...
 2.23: In Exercises 2223, let f(x)=3x 7 and g(x) = x3 + 1 to find a formul...
 2.24: In Exercises 2425, give the meaning and units of the composite func...
 2.25: In Exercises 2425, give the meaning and units of the composite func...
 2.26: In Exercises 2633, use f(x) = x2 + 1 and g(x)=2x + 3. f(g(0))
 2.27: In Exercises 2633, use f(x) = x2 + 1 and g(x)=2x + 3.f(g(1))
 2.28: In Exercises 2633, use f(x) = x2 + 1 and g(x)=2x + 3.g(f(0))
 2.29: In Exercises 2633, use f(x) = x2 + 1 and g(x)=2x + 3.g(f(1))
 2.30: In Exercises 2633, use f(x) = x2 + 1 and g(x)=2x + 3.f(g(x))
 2.31: In Exercises 2633, use f(x) = x2 + 1 and g(x)=2x + 3.g(f(x))
 2.32: In Exercises 2633, use f(x) = x2 + 1 and g(x)=2x + 3.f(f(x))
 2.33: In Exercises 2633, use f(x) = x2 + 1 and g(x)=2x + 3.g(g(x))
 2.34: In Exercises 3435, give the meaning and units of the inverse functi...
 2.35: In Exercises 3435, give the meaning and units of the inverse functi...
 2.36: In Exercises 3637, find the domain and range of the function.g(x) =...
 2.37: In Exercises 3637, find the domain and range of the function.q(x)=(...
 2.38: In Exercises 3839, find the inverse function.y = g(t) = t + 1
 2.39: In Exercises 3839, find the inverse function.P = f(q) = 14q 2
 2.40: In Exercises 4042, let P = f(t) be the population, in millions, of ...
 2.41: In Exercises 4042, let P = f(t) be the population, in millions, of ...
 2.42: In Exercises 4042, let P = f(t) be the population, in millions, of ...
 2.43: Calculate successive rates of change for the function, p(t), in Tab...
 2.44: If p(x) = 12 x , evaluate p(8) and p1( 2)
 2.45: For f(x) = 12 x, evaluate f(16) and f1(3).
 2.46: In Exercises 4647, graph the function.f(x) = x2 for x 1 2 x for x > 1
 2.47: In Exercises 4647, graph the function.g(x) = x + 5 for x < 0 x2 + 1...
 2.48: If V = 1 3 r2h gives the volume of a cone, what is the value of V w...
 2.49: Let q(x)=3 x2. Evaluate and simplify: (a) q(5) (b) q(a) (c) q(a 5) ...
 2.50: Let p(x) = x2 +x+ 1. Find p(1) and p(1). Are they equal?
 2.51: Chicagos average monthly rainfall, R = f(t) inches, is given as a f...
 2.52: Use the graph of f(x) in Figure 2.30 to estimate: (a) f(0) (b) f(1)...
 2.53: Let f(x) = x2 + 16 5. (a) Find f(0) (b) For what values of x is f(x...
 2.54: Use the graph in Figure 2.31 to fill in the missing values: (a) f(0...
 2.55: Use the values of the invertible function in Table 2.23 to find as ...
 2.56: The formula V = f(r) = 4 3 r3 gives the volume of a sphere of radiu...
 2.57: The formula for the volume of a cube with side s is V = s3. The for...
 2.58: The area, A = f(s) ft2, of a square wooden deck is a function of th...
 2.59: Table 2.24 shows the cost, C(m), in dollars, of a taxi ride as a fu...
 2.60: The perimeter, in meters, of a square whose side is s meters is giv...
 2.61: (a) Find the side, s = f(d), of a square as a function of its diago...
 2.62: Suppose that j(x) = h1(x) and that both j and h are defined for all...
 2.63: Let k(x)=6 x2. (a) Find a point on the graph of k(x) whose xcoordin...
 2.64: (a) Find a point on the graph of h(x) = x + 4 whose xcoordinate is...
 2.65: Let t(x) be the time required, in seconds, to melt 1 gram of a comp...
 2.66: (a) The Fibonacci sequence is a sequence of numbers that begins 1, ...
 2.67: A psychologist conducts an experiment to determine the effect of sl...
 2.68: Give a formula for a function whose domain is all nonnegative value...
 2.69: Give a formula for a function that is undefined for x = 8 and for x...
 2.70: Many printing presses are designed with large plates that print a f...
 2.71: Table 2.25 shows the population, P, in millions, of Ireland16 at va...
Solutions for Chapter 2: FUNCTIONS
Full solutions for Functions Modeling Change: A Preparation for Calculus  4th Edition
ISBN: 9780470484753
Solutions for Chapter 2: FUNCTIONS
Get Full SolutionsThis textbook survival guide was created for the textbook: Functions Modeling Change: A Preparation for Calculus , edition: 4. Since 71 problems in chapter 2: FUNCTIONS have been answered, more than 25435 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 2: FUNCTIONS includes 71 full stepbystep solutions. Functions Modeling Change: A Preparation for Calculus was written by and is associated to the ISBN: 9780470484753.

Arccosine function
See Inverse cosine function.

Center
The central point in a circle, ellipse, hyperbola, or sphere

Continuous function
A function that is continuous on its entire domain

Division algorithm for polynomials
Given ƒ(x), d(x) ? 0 there are unique polynomials q1x (quotient) and r1x(remainder) ƒ1x2 = d1x2q1x2 + r1x2 with with either r1x2 = 0 or degree of r(x) 6 degree of d1x2

Endpoint of an interval
A real number that represents one “end” of an interval.

equation of a quadratic function
ƒ(x) = ax 2 + bx + c(a ? 0)

Geometric sequence
A sequence {an}in which an = an1.r for every positive integer n ? 2. The nonzero number r is called the common ratio.

Horizontal component
See Component form of a vector.

Horizontal translation
A shift of a graph to the left or right.

Identity matrix
A square matrix with 1’s in the main diagonal and 0’s elsewhere, p. 534.

Logarithmic function with base b
The inverse of the exponential function y = bx, denoted by y = logb x

Magnitude of a vector
The magnitude of <a, b> is 2a2 + b2. The magnitude of <a, b, c> is 2a2 + b2 + c2

nth power of a
The number with n factors of a , where n is the exponent and a is the base.

Numerical model
A model determined by analyzing numbers or data in order to gain insight into a phenomenon, p. 64.

Octants
The eight regions of space determined by the coordinate planes.

Power function
A function of the form ƒ(x) = k . x a, where k and a are nonzero constants. k is the constant of variation and a is the power.

Product of complex numbers
(a + bi)(c + di) = (ac  bd) + (ad + bc)i

Root of an equation
A solution.

Sum of a finite arithmetic series
Sn = na a1 + a2 2 b = n 2 32a1 + 1n  12d4,

xcoordinate
The directed distance from the yaxis yzplane to a point in a plane (space), or the first number in an ordered pair (triple), pp. 12, 629.