Free Printable Unit 3 Test Review

1.

a)

-4

b)

0, -4

c)

4

d)

0, 4

2.

a)

x = 2 , x = 1

b)

x = 1

c)

x = 2

d)

x = 2 , x = -1

3.

a)

x = -3, x = 1

b)

x = -1 , x = -3

c)

x = 1 , x = 3

d)

x = -1, x = 3

4.

a)

x = - 9, x = 7

b)

x = 7

c)

x = 9

d)

x = 9, x = - 7

5.

a)

n = 5 and -6

b)

n = -6

c)

n = 5

d)

No Solution

6.

a)

14

b)

-14

c)

6

d)

-6

7.

a)

4

b)

-4

c)

2

d)

-2

8.

a)

20

b)

11

c)

4

d)

-2

9.

a)

5

b)

33

c)

85

d)

21

10.

Solve the following equation.
$\sqrt{2x+4}=-10$

a)

48

b)

49

c)

No Solution

d)

52

11.

Solve the following equation.
$2\sqrt{x+1}-3=-9$

a)

8

b)

35

c)

-2

d)

No Solution

12.

a)

7²

b)

7^1/2

c)

7^-2

d)

7^-1/2

13.

a)

4^4/3

b)

4^3/4

c)

2^4/3

d)

2^3/4

14.

Write in exponential form
√x⁵

a)

X¹∕ ⁵

b)

X ²⁄⁵

c)

X⁵⁄ ²

d)

X⁵

15.

Write the following expression in radical form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

16.

Write the following expression in exponential form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

17.

Write the following expression in radical form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

18.

Write the following expression in exponential form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

19.

Write using a rational exponent: $\sqrt[3]{x^6}$

a)

$x^2$

b)

$x^3$

c)

$x^9$

d)

$x^{\frac{1}{2}}$

20.

Write using a rational exponent: $\sqrt[]{x^{12}}$

a)

$x^6$

b)

$x^{\frac{1}{12}}$

c)

$x^{\frac{1}{6}}$

d)

$x^{12}$

21.

Write using a radical: $x^{\frac{3}{7}}$

a)

$\sqrt[7]{x^3}$

b)

$\sqrt[3]{x^7}$

c)

$\sqrt[]{x^{\frac{7}{3}}}$

d)

$x^4$

22.

Given the function, which of the following correctly describes the transformations?

a)

reflection over the x-axis, vertical stretch by 3, horizontal shift left 1 and vertical shift down 5

b)

reflection over the y-axis, vertical stretch by 1/3, horizontal shift left 1 and vertical shift down 5

c)

reflection over the x-axis, vertical compression by 1/3, horizontal shift left 1 and vertical shift down 5

d)

reflection over the x-axis, vertical stretch by 1/3, horizontal shift right 1 and vertical shift down 5

23.

Compare the two functions below. Which function has a domain x ≥ 1?

a)

f(x)

b)

g(x)

c)

Neither function

d)

Cannot be determined from the graph alone.

24.

Which equation matches the graph

a)

f\left(x\right)=^{ }\sqrt{x-6}

b)

$f\left(x\right)=^{ }\sqrt{x+6}$

c)

$f\left(x\right)=^{ }\sqrt{x}+6$

d)

$f\left(x\right)=^{ }\sqrt{x}-6$

25.

What is the domain of the graph of the radical function?

a)

(-infinity, infinity)

b)

[-7, infinity)

c)

[0, infinity)

d)

[4, infinity)

26.

What transformations of the parent function,

y=\sqrt{x}

is the function

g\left(x\right)\ =2\sqrt{x+5}

?

a)

Vertical stretch and a horizontal shift left 5

b)

Vertical stretch and a horizontal shift right 5

c)

Vertical compression and a horizontal shift left 5

d)

Vertical stretch and a vertical shift up 5

27.

Match the correct equation with the given graph.

a)

$y=\sqrt{x}+2$

b)

y = √(x) - 2

c)

y = √(x + 2)

d)

y = √(x - 2)

28.

Which of these equations shifts a radical equation right 5 times and down once?

a)

y = √(x - 5) - 1

b)

y = √(x + 5) - 1

c)

y = √(x - 5) + 1

d)

y = √(x + 5) + 1

29.

Simplify. $\frac{27^{\frac{4}{3}}}{27^{\frac{2}{3}}}$

a)

9

b)

3

c)

140.3

d)

19683

30.

Simplify. $4^{\frac{3}{2}}\cdot4^{\frac{5}{2}}$

a)

65536

b)

16

c)

4096

d)

256

31.

Which operation is the opposite of a radical?

a)

Addition

b)

Subtraction

c)

Exponent

d)

Division

e)

Multiplication

32.

Write the inverse function. $y=\left(2x-1\right)^{\frac{1}{3}}+7$

a)

$y=\frac{\left(x+7\right)^3-1}{2}$

b)

$y=\frac{\left(x+1\right)^3+7}{2}$

c)

$y=\frac{\left(x-1\right)^3+7}{2}$

d)

$y=\frac{\left(x-7\right)^3+1}{2}$

33.

Write the inverse function. $y=\left(x+3\right)^{\frac{1}{2}}$

a)

$y\ =x^2-3$

b)

$y=x^2+3$

c)

$y=\sqrt{x-3}$

d)

$y=\sqrt{x+3}$

34.

What is the first step when solving the radical equation $4\sqrt{x-7}+\ 12\ =\ 28$

a)

Divide both sides of the equation by 4

b)

Square both sides of the equation

c)

Subtract 12 from both sides of the equation

d)

Add 7 to both sides of the equation

e)

Check your solution

35.

Are these the graphs of two inverse functions?

a)

Yes

b)

No

c)

No way to tell

36.

Are these functions inverses?

a)

No

b)

Yes

c)

No way to tell

37.

Which graph represents the functions f(x) and f^-1(x)?

a)

b)

c)

38.

What are the transformations of this functions compared to the parent function?

a)

Shifted down 2

b)

Shifted up 2

c)

Shifted left 2

d)

Shifted right 2

39.

What is the DOMAIN of the function?

a)

[-3, infinity)

b)

[0, infinity)

c)

[3, inifinity)

d)

(-infinity, 0}

40.

What is the RANGE of the function?

a)

(- ∞, -2 ]

b)

[ -2, ∞ )

c)

All Real Numbers

d)

[ 0, ∞)

41.

What is the y-intercept of the graph?

a)

(-1,0)

b)

(0,-1)

c)

(0,3)

d)

(3,0)

42.

The inverse has been reflected over which line?

a)

y = x

b)

y =1

c)

y = 0

d)

y = x + 1

43.

What is the y-intercept of the function

f\left(x\right)=\sqrt{x+4}+1

?

a)

$\left(0,0\right)$

b)

$\left(0,3\right)$

c)

$\left(3,0\right)$

d)

$None$

44.

What is the DOMAIN of this square root function?

a)

all real numbers

b)

$x\ge1$

c)

$x\le1$

d)

$x\ge2$

45.

What is the RANGE of this square root function?

a)

all real numbers

b)

$y\ge1$

c)

$y\le2$

d)

$y\ge2$

46.

Solve the cube root equation

a)

$x=344$

b)

$x=21$

c)

$x=-344$

d)

$x=-21$

47.

Solve the cube root equation

a)

$x=36$

b)

$x=-216$

c)

$x=216$

d)

$x=-36$

48.

The length of a standard nail in inches can be modeled by $L=54d^{\frac{3}{2}}$ , where d is the diameter in inches of the nail. What is the diameter of a standard nail that is 8 inches long?

a)

0.28 inches

b)

0.06 inches

c)

1221.88 inches

d)

12.84 inches

Unit 3 Test Review

Total questions: 48

Worksheet time: 5hrs 23mins

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