Free Printable Unit 2 TEST Review

1.

When f(x) = 9 - 3x and g(x) = 5x - 7

find f(x) + g(x).

a)

14x - 10

b)

-8x + 2

c)

2x + 2

d)

2x - 2

2.

When f(x) = x²+ 9 and g(x) = x - 9,

find f(x) - g(x).

a)

x²+ x + 9

b)

x²- x + 9

c)

x²- x

d)

x²- x + 18

3.

f(x)=2x + 4

g(x)=3x²- 1

Find f(x) ⋅ g(x)

a)

6x⁴+ 12x³- 4x²- 8x

b)

-6x³+ 12x²+ 2x - 4

c)

6x³+ 12x²- 2x - 4

d)

5x²- 18x + 20

4.

f(x) = 4x + 8

g(x) = x + 3,

Find f(x) ⋅ g(x)

a)

4x²+ 24

b)

4x²+ 20x + 24

c)

4x²+ 12x + 24

d)

4x²+ 4x + 24

5.

Perform the indicated operation.

a)

b)

c)

d)

6.

Complete the operation and evaluate.

a)

b)

c)

d)

7.

Perform the indicated operation and evaluate for the given value.

a)

b)

c)

d)

8.

Perform the indicated operation.

a)

b)

c)

d)

9.

Perform the indicated operation and evaluate at the given value.

a)

b)

c)

d)

10.

Given the functions

f\left(x\right)=x^2+5

and

g\left(x\right)=4x-9

find

\frac{f}{g}

a)

$\frac{4x-9}{x^2+5}$

b)

$\frac{x^2+5}{4x-9}$

c)

$\frac{x^2}{4x}$

d)

$-\ \frac{5}{9}$

11.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $f\left(g\left(3\right)\right)$

a)

34

b)

71

c)

35

d)

142

12.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $g\left(f\left(-1\right)\right)$

a)

2

b)

15

c)

7

d)

-9

13.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $f\left(g\left(x\right)\right)$

a)

$4x^2-1$

b)

$4x^2-2$

c)

$8x^2-1$

d)

$16x^2-1$

14.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=3x+2$ find $\left(g\circ f\right)\left(x\right)$

a)

$\frac{1}{3x}+2$

b)

$3x+2$

c)

$\frac{3}{x}+2$

d)

$\frac{1}{3x+2}$

15.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=3x+2$ find $f\left(g\left(x\right)\right)$

a)

$\frac{1}{3x}+2$

b)

$3x+2$

c)

$\frac{3}{x}+2$

d)

$\frac{1}{3x+2}$

16.

If $f\left(x\right)=x^2$ and $g\left(x\right)=\sqrt{x}$ find $g\left(f\left(x\right)\right)$

a)

$x^4$

b)

$x$

c)

$\sqrt[]{x}$

d)

$x^2$

17.

When $f(x)=x^2+9$ and $g(x)=x-9$ , find $f(x)-g(x)$

a)

$x^2+x+9$

b)

$x^2-x+9$

c)

$x^2-x$

d)

$x^2-x+18$

18.

$f\left(x\right)=3x$
Find $f^{-1}\left(x\right)$

a)

$\frac{x}{3}$

b)

$\frac{3}{x}$

c)

$0.3x$

d)

$x\times3$

19.

$f\left(x\right)=5x+1$
Find $f^{-1}\left(x\right)$

a)

$\frac{x-5}{1}$

b)

$\frac{x}{5}-1$

c)

$x-\frac{1}{5}$

d)

$\frac{x-1}{5}$

20.

$f\left(x\right)=\frac{x-2}{6}$
Find $f^{-1}\left(x\right)$

a)

$\frac{x-6}{2}$

b)

$6x+2$

c)

$2x+6$

d)

$6\left(x+2\right)$

21.

$f\left(x\right)=\frac{8x-3}{5}$
Find $f^{-1}\left(x\right)$

a)

$5\left(8x+3\right)$

b)

$\frac{5x}{8}+3$

c)

$\frac{5\left(x+3\right)}{8}$

d)

$\frac{5x+3}{8}$

22.

What are the inverse points for the coordinates:

(3, 0) , (2, -4), (5, 5) and (-6,8)

a)

(3,0) , (2, -4) , (5,5) , (6,8)

b)

(0,3) , (-4,2) , (5,5) , (8,-6)

c)

(3,2), (0, -4), (5, -6), (5,8)

23.

What is the FIRST step I need to take to solve for x in the following equation?

a)

Add 9 to both sides

b)

Take the square root of both sides

c)

Divide both sides by 49

d)

Multiply both sides by 9

24.

a)

Inverse Functions

b)

Not Inverse Functions

25.

$f\left(x\right)=\frac{3x+10}{7}$
Find $f^{-1}\left(x\right)$

a)

$7x-\frac{10}{3}$

b)

$\frac{7x}{3}-10$

c)

$\frac{7\left(x-10\right)}{3}$

d)

$\frac{7x-10}{3}$

26.

$f\left(x\right)=\frac{6x}{5}+3$
Find $f^{-1}\left(x\right)$

a)

$\frac{5x-3}{6}$

b)

$\frac{5\left(x-3\right)}{6}$

c)

$\frac{5x}{6}-3$

d)

$\frac{5x}{6}+3$

27.

a)

Inverse Functions

b)

Not Inverse Functions

28.

Which equation below is a quadratic function translated up 5 units?

a)

y = x² + 5

b)

y = (x + 5)²

c)

y = 5x²

d)

y = -x² - 5

29.

Describe the transformation

a)

left 2 up 5

b)

right 2 up 5

c)

left 2 down 5

d)

right 2 down 5

30.

Tell how the function transformed from y =|x|
y = -2|x|

a)

Translated left 2 units

b)

Reflected over x-axis

c)

Stretched vertically and reflected over x-axis

d)

Compressed vertically and reflected over the x-axis

31.

Write the equation that results if the parent absolute value function is shifted right 15 units, down 3 units, and reflected vertically.

a)

$y=-\left|x-15\right|-3$

b)

$y=-\left|x+15\right|-3$

c)

$y=\frac{1}{2}\left|x+3\right|-15$

d)

$y=\frac{1}{2}\left|x-3\right|-15$

e)

$y=\left|-x-15\right|-3$

32.

What is the equation of the PARENT function?

a)

f(x) = 2^x

b)

f(x) = x³

c)

f(x) = |x|

d)

f(x) = x

33.

Describe the transformation(s) in the following function.

$f\left(x\right)=\frac{4}{5}\left|x+5\right|+2$

a)

Vertical stretch by a factor of $\frac{4}{5}$ ,

Shift left 5 units,

Shift down 2 units

b)

Vertical compression by a factor of $\frac{4}{5}$ ,

Shift right 5 units,

Shift up 2 units

c)

Vertical stretch by a factor of $\frac{4}{5}$ ,

Shift right 5 units,

Shift up 2 units

d)

Vertical compression by a factor of $\frac{4}{5}$ ,

Shift left 5 units,

Shift up 2 units

e)

Vertical compression by a factor of $\frac{4}{5}$ ,

Shift left 5 units,

Shift down 2 units

34.

Describe the transformation from the parent graph

a)

Reflect over x, right 3, down 4

b)

Reflect over y, right 3, down 4

c)

Reflect over x, right 3, up 4

d)

Reflect over y, left 3, down 4

35.

What type of function is shown?

a)

cube root

b)

square root

c)

logarithm

d)

exponential

36.

Describe the transformation that is applied to the parent function. $f(x)=\left|x\right|-5$

a)

Shifts left 5

b)

Shifts right 5

c)

Shifts up 5

d)

Shifts down 5

37.

What shifts have occurred?

a)

left 1, up 5

b)

left 1, down 5

c)

right 1, down 5

d)

right 1, up 5

38.

Write the equation that results if the parent absolute value function is shifted right 15 units, down 3 units, and reflected vertically.

a)

$y=-\left|x-15\right|-3$

b)

$y=-\left|x+15\right|-3$

c)

$y=\frac{1}{2}\left|x+3\right|-15$

d)

$y=\frac{1}{2}\left|x-3\right|-15$

e)

$y=\left|-x-15\right|-3$

39.

Describe the transformation of the equation below from the absolute value parent function $y=-2\left|x-3\right|+3$

a)

reflected over x axis, stretched by 2, right 3, up 3

b)

reflected over x axis, stretched by 2, left 3 up 3.

c)

reflected over x axis, shrunk by 2, right 3, up 3

d)

reflected over the x axis, shrunk by 2, left 3, up 3

40.

Describe the transformation that is applied to the parent function.

$f(x)=3\left|x+8\right|$

a)

Stretches by 3, Shifts left 8

b)

Stretches by 3, Shifts right 8

c)

Stretches by 3, Shifts up 8

d)

Stretches by 3, Shifts down 8

41.

Which of the following graphs is the parent function to the function

$f\left(x\right)=2\left|x-2\right|+6$ ?

a)

b)

c)

d)

42.

$\frac{5}{x}$ What is the restricted domain?

a)

$x\ne5$

b)

$x\ne0$

c)

$x\ge5$

d)

$x\ge0$

43.

$\frac{3}{x+4}$ What is the restricted domain?

a)

$x\ge4$

b)

$x\ge3$

c)

$x\ne3$

d)

$x\ne-4$

44.

$\frac{5}{\sqrt{x-2}}$ Choose the domain for which the function is defined.

a)

$x\ne2$

b)

$x\ne5$

c)

$x\ge2$

d)

$x\ge5$

45.

$\frac{1}{\sqrt{x+4}}$ Choose the domain for which the function is defined?

a)

$x\ge-4$

b)

$x\le4$

c)

$x\ge4$

d)

$x\le-4$

Unit 2 TEST Review

Total questions: 45

Worksheet time: 1hrs 28mins

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