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88
Chapter 1
Functions and Their Graphs
1 Chapter Test
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.
4
−4
8
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.
y2(4 − x) = x3
−4
Figure for 3
4. Evaluate f x x 2 15 at each value of the independent variable and simplify.
(a) f 8
(b) f 14
(c) f t 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 sold, 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. f x 2x3 3x
8. f x 3x4 5x2
In Exercises 9 and 10, determine the open intervals on which the function is increasing, decreasing, or constant.
9. hx 14x 4 2x 2
10. gt 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 x3 5x2 12
12. f x x5 x3 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. gx 2x 53 3
16. Use the functions f x domain.
(a) f gx
(b)
14. gx x 7
x2
and gx 2 x to find the specified function and its
g x
f
15. g x 4 x 7
(c) f gx
(d) g f x
In Exercises 17–19, determine whether the function has an inverse function, and if
so, find the inverse function.
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10:10 pm Tues
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Y
t
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Sbscribers, S
9
10
11
12
13
14
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109.5
128.4
140.8
158.7
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17. f x x3 8
18. f x x2 6
19. f x 3xx
8
20. The table shows the numbers of cellular phone subscribers S (in millions) in the
United States from 1999 through 2004, where t represents the year, with t 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)
Table for 20