College Algebra with Corequisite Support 2e

# Practice Test

### Practice Test

For the following exercises, determine whether each of the following relations is a function.

1 .

$y=2x+8 y=2x+8$

2 .

${ (2,1),(3,2),(−1,1),(0,−2) } { (2,1),(3,2),(−1,1),(0,−2) }$

For the following exercises, evaluate the function $f(x)=−3 x 2 +2x f(x)=−3 x 2 +2x$ at the given input.

3 .

$f(−2) f(−2)$

4 .

$f(a) f(a)$

5 .

Show that the function $f(x)=−2 (x−1) 2 +3 f(x)=−2 (x−1) 2 +3$ is not one-to-one.

6 .

Write the domain of the function $f(x)= 3−x f(x)= 3−x$ in interval notation.

7 .

Given $f(x)=2 x 2 −5x, f(x)=2 x 2 −5x,$ find $f(a+1)−f(1) f(a+1)−f(1)$ in simplest form.

8 .

Graph the function

9 .

Find the average rate of change of the function $f(x)=3−2 x 2 +x f(x)=3−2 x 2 +x$ by finding $f(b)−f(a) b−a f(b)−f(a) b−a$ in simplest form.

For the following exercises, use the functions to find the composite functions.

10 .

$( g∘f )(x) ( g∘f )(x)$

11 .

$( g∘f )(1) ( g∘f )(1)$

12 .

Express $H(x)= 5 x 2 −3x 3 H(x)= 5 x 2 −3x 3$ as a composition of two functions, $f f$ and $g, g,$ where $( f∘g )(x)=H(x). ( f∘g )(x)=H(x).$

For the following exercises, graph the functions by translating, stretching, and/or compressing a toolkit function.

13 .

$f(x)= x+6 −1 f(x)= x+6 −1$

14 .

$f(x)= 1 x+2 −1 f(x)= 1 x+2 −1$

For the following exercises, determine whether the functions are even, odd, or neither.

15 .

$f(x)=− 5 x 2 +9 x 6 f(x)=− 5 x 2 +9 x 6$

16 .

$f(x)=− 5 x 3 +9 x 5 f(x)=− 5 x 3 +9 x 5$

17 .

$f(x)= 1 x f(x)= 1 x$

18 .

Graph the absolute value function $f(x)=−2| x−1 |+3. f(x)=−2| x−1 |+3.$

For the following exercises, find the inverse of the function.

19 .

$f(x)=3x−5 f(x)=3x−5$

20 .

$f(x)= 4 x+7 f(x)= 4 x+7$

For the following exercises, use the graph of $g g$ shown in Figure 1.

Figure 1
21 .

On what intervals is the function increasing?

22 .

On what intervals is the function decreasing?

23 .

Approximate the local minimum of the function. Express the answer as an ordered pair.

24 .

Approximate the local maximum of the function. Express the answer as an ordered pair.

For the following exercises, use the graph of the piecewise function shown in Figure 2.

Figure 2
25 .

Find $f(2). f(2).$

26 .

Find $f(−2). f(−2).$

27 .

Write an equation for the piecewise function.

For the following exercises, use the values listed in Table 1.

 $x x$ 0 1 2 3 4 5 6 7 8 $F(x) F(x)$ 1 3 5 7 9 11 13 15 17
Table 1
28 .

Find $F(6). F(6).$

29 .

Solve the equation $F(x)=5. F(x)=5.$

30 .

Is the graph increasing or decreasing on its domain?

31 .

Is the function represented by the graph one-to-one?

32 .

Find $F −1 (15). F −1 (15).$

33 .

Given $f(x)=−2x+11, f(x)=−2x+11,$ find $f −1 (x). f −1 (x).$