88 Chapter 1 Functions and Their Graphs 1 Cha pter 153 See www.CalcChat.com for worked-out solutions to odd-numbered exercises. Take this test as you would take a test in class. After you are finished, check your work against the answers in the back of the book. 1. Find the equations of the lines that pass through the point (0. 4) and are (a) parallel to and (b) perpendicular to the line 5x + 2y = 3. 2. Find the slope-intercept form of the equation of the line that passes through the points (2, 1) and (-3, 4). 3. Does the graph at the right represent y as a function of x? Explain. 4, Evaluate f(x) = |x + 2| 15 at each value of the independent variable and simplify. @ f(=8) ) f(14) (o) ft 6) 5. Find the domain of f(x) = 10 /3 x. 6. An electronics company produces a car stereo for which the variable cost is $5.60 and the fixed costs are $24,000. The product sells for $99.50. Write the total cost C as a function of the number of units produced and seld, x. Write the profit P as a function of the number of units produced and sold, x. In Exercises 7 and 8, determine algebraically whether the function is even, odd, or neither. 7. flx) = 2x* 3x 8. f(x) = 3x* + 522 In Exercises 9 and 10, determine the open intervals on which the function is increas- ing, decreasing, or constant. 9. hx) = txt 242 10. g() = |t +2| |t - 2] In Exercises 11 and 12, use a graphing utility to graph the functions and to approximate (to two decimal places) any relative minimum or relative maximum values of the function. 11. f(x) = x* 522 + 12 12. f) = x4+ 2 In Exercises 13-15, (a) identify the parent function f, (b) describe the sequence of transformations from f to g, and (c) sketch the graph of g. 13. g(x) = 2(x 5 + 3 4. gx) = Vx7 15. g(x) = 4|x| = 7 16. Use the functions f(x) = x? and g(x) = /2 x to find the specified function and its domain, @-g0 oo uon @k In Exercises 17-19, determine whether the function has an inverse function, and if so, find the inverse function. 3x/x 17. f(x) =x* + 8 18. fx) = + 6 19. flo) = = 20. The table shows the numbers of cellular phone subscribers (in millions) in the United States from 1999 through 2004, where represents the year, with =9 corresponding to 1999. Use the regression feature of a graphing utility to find a linear model for the data. Use the model to find the year in which the number of subscribers exceeded 200 million. (Source: Cellular Telecommunications & Internet Association) V4 -x)=x3 -4 4 Figure for 3 Subscribers, S Table for 20 86.0 109.5 128.4 140.8 158.7 182.1