Free Printable Unit 5 Review

1.

Rewrite in radical form.

a)

A

b)

B

c)

C

d)

D

2.

Rewrite in Exponential Form.

a)

A

b)

B

c)

C

d)

D

3.

Rewrite in Exponential Form.

a)

A

b)

B

c)

C

d)

D

4.

Evaluate without a calculator.

a)

A

b)

B

c)

C

d)

D

5.

$x^0=$

a)

0

b)

1

c)

x

d)

-x

6.

Select all the expressions that are equivalent to $4^{-3}$ .

a)

$-12$

b)

$\frac{1}{64}$

c)

$-64$

d)

$\frac{1}{4^3}$

e)

$64$

7.

$\sqrt{64}=$

a)

$32$

b)

$4$

c)

$8$

d)

$64^2$

8.

Evaluate.

a)

20

b)

200

c)

√200

d)

±20

9.

∛125

a)

5

b)

4

c)

6

d)

7

10.

Evaluate.

a)

444

b)

222

c)

4

d)

2

11.

Simplify:

a)

28

b)

56

c)

11

d)

15

12.

Simplify:

a)

41

b)

17

c)

23

d)

15

13.

∛8

(a)

14.

(x⁴)²

a)

x⁸

b)

x⁶

c)

x²

d)

8

15.

(6x²)(-3x⁵)

a)

18x⁷

b)

-18x⁷

c)

18x⁷

d)

3x⁷

16.

According to exponent rules, when we raise a power to a power we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

17.

According to exponent rules, when we multiply powers we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

18.

8⁰ = 0

a)

True

b)

False

19.

Can you leave a negative exponent in your answer?

a)

YES

b)

NO

20.

Simplify using your exponent rule(s) x⁻⁶

a)

1 ⁄ x⁶

b)

x⁶

c)

-x⁶

d)

-1 ⁄ x⁶

21.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

22.

According to exponent rules, when we raise the power to a power we _______ the exponents.
Example: (d²)⁵

a)

add

b)

subtract

c)

multiply

d)

divide

23.

According to exponent rules, when we multiply two power with the same base we _______ the exponents.
Example: c⁶ ⋅ c⁴

a)

add

b)

subtract

c)

multiply

d)

divide

24.

Simplify:

a)

6

b)

12

c)

36

d)

432

25.

Simplify . Your answer should contain only positive exponents. $\left(x^0y^{\frac{1}{3}}\right)^{\frac{3}{2}}x^0$

a)

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

b)

$1$

c)

$y^{\frac{4}{3}}$

d)

$0$

26.

Evaluate 8^2/3

a)

2

b)

3

c)

4

d)

5

27.

Simplify. Your answer should only contain positive exponents.

a)

A

b)

B

c)

C

d)

D

28.

(x^2/3)⁴

a)

x^8/3

b)

x^8/12

c)

x⁸

d)

x³

29.

a)

a

b)

b

c)

c

d)

d

30.

$\left(\frac{x^2}{5}\right)^3$

a)

$\frac{x^6}{125}$

b)

$\frac{x^5}{15}$

c)

$\frac{x^5}{8}$

d)

$\frac{x^6}{15}$

31.

\left(\frac{z^5}{r}\right)^3

a)

$\frac{z^{15}}{r^3}$

b)

$\frac{z^{15}}{r}$

c)

$\frac{z^8}{r^4}$

d)

$\frac{z^8}{r^4}$

32.

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

a)

$\frac{x^{21}}{y^{14}}$

b)

$\frac{x^{10}}{y^9}$

c)

$\frac{x^4}{y^5}$

d)

$\frac{7x^3}{7y^2}$

33.

Exponent Rules: Product Rule

a^x\cdot a^y=

a)

$a^{x\cdot y}$

b)

$a^{x+y}$

c)

$a^x+a^y$

34.

Exponent Rules: Quotient Rule

\frac{a^x}{a^y}=

a)

$a^{x-y}$

b)

$a^{\frac{x}{y}}$

c)

$a^{x+y}$

35.

Exponent Rules: Power of a Power Rule

a^{x^y}\ or\ \left(a^x\right)^y\ =

a)

$a^{x+y}$

b)

$a^{x\cdot y}$

c)

$a^xa^y$

36.

Exponent Rules: Power of a Product

\left(ab\right)^x=

a)

$a^x+b^x$

b)

$a^{bx}$

c)

$a^xb^x$

37.

Exponent Rules: Negative Exponent

a^{-x}=

a)

$-a^{-x}$

b)

$-a^x$

c)

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

d)

$-\frac{1}{a^x}$

38.

Exponent Rules: RATIONAL EXPONENT

a^{\frac{x}{y}}=

a)

$\ ^y\sqrt{a^x}$

b)

$a^x-a^y$

c)

$\frac{a^x}{a^y}$

39.

$\left(x^{\frac{1}{2}}y^{\frac{1}{4}}z^{\frac{1}{3}}\right)^{12}\ =$

Simplify the following:

a)

$x^{12.5}y^{12.25}z^{12.33}$

b)

$12\left(x^{\frac{1}{2}}y^{\frac{1}{4}}z^{\frac{1}{3}}\right)$

c)

$x^6y^3z^4$

40.

$\left(8x^9\right)^{\frac{2}{3}}$

a)

$22x^{\frac{27}{2}}$

b)

$8x^6$

c)

$4x^6$

d)

$x^6$

41.

Simplify

a)

x²y√xy

b)

xy

c)

x²y²

d)

Can't Simplify

42.

Simplify

a)

3x²y²z√3yz

b)

3xyz√xy²

c)

3xyz

d)

Can't Simplify

43.

Simplify:
√160

a)

4√5

b)

4√10

c)

10√4

d)

8√10

44.

Simplify the radical...
√20a²b⁴

a)

2ab²√5

b)

4ab²√5

c)

5ab²√2

d)

2a²b²√5

45.

a)

A

b)

B

c)

C

d)

D

46.

a)

A

b)

B

c)

C

d)

D

47.

a)

A

b)

B

c)

C

d)

D

48.

a)

A

b)

B

c)

C

d)

D

49.

a)

A

b)

B

c)

C

d)

D

50.

Simplify:
6√2 ⋅5√14

a)

32√7

b)

60√7

c)

2√7

d)

30√7

51.

Simplify

a)

b)

c)

d)

e)

52.

Simplify

a)

b)

c)

d)

e)

53.

Simplify:
√6 ⋅√6

a)

√36

b)

2√3

c)

12

d)

6

54.

Simplify $2\sqrt{27}\cdot3\sqrt{3}$

a)

$5\sqrt{81}$

b)

$54$

c)

$9\sqrt{3}$

d)

$3\sqrt{3}$

55.

Simplify:

\sqrt{x^2y^7}

a)

$xy^3$

b)

$xy^3\sqrt{y}$

c)

$xy^3\sqrt{xy}$

56.

Simplify:

\sqrt{80x^2y^4}

a)

$2xy^2\sqrt{20}$

b)

$4xy^2\sqrt{5}$

57.

Simplify
3√8 + 3√2

a)

9√2

b)

6√10

c)

5√2

d)

Already simplified

58.

Simplify
3√6 - 4√6

a)

-√6

b)

√6

c)

-1

d)

Already simplified

59.

Simplify
-3√20 - √5

a)

-4√5

b)

-4√15

c)

-7√5

d)

Already simplified

60.

Simplify
3√18 - 2√2

a)

7√2

b)

√16

c)

√2

d)

Already simplified

61.

What is the conjugate of:
$5+\sqrt{7}$

a)

18

b)

$5+\sqrt{7}$

c)

$5-\sqrt{7}$

d)

32

62.

Multiply:
$\left(4+\sqrt{2}\right)\left(4-\sqrt{2}\right)$

a)

$16-\sqrt{2}$

b)

$4-\sqrt{2}$

c)

14

d)

18

63.

What should you multiply $\frac{6}{1-\sqrt{5}}$ by to rationalize the denominator?

a)

-4

b)

$1-\sqrt{5}$

c)

$1+\sqrt{5}$

d)

$-\frac{\left(3-3\sqrt{5}\right)}{2}$

64.

What should you multiply $\frac{3\sqrt{2}}{2-\sqrt{7}}$ by to rationalize the denominator?

a)

$2-\sqrt{7}$

b)

$\sqrt{7}$

c)

$2+\sqrt{7}$

d)

$\sqrt{2}$

65.

$\frac{-2}{1+\sqrt{6}}$ Rationalize the following:

a)

$\frac{1+\sqrt{6}}{-2}$

b)

$\frac{-2+2\sqrt{6}}{-5}$

c)

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

d)

$-2\sqrt{6}$

66.

Simplify.

a)

b)

c)

d)

67.

What is the parent function of square root functions?

a)

f(x) = x

b)

f(x) = √x

c)

f(x) = -√x

d)

f(x) = x²

68.

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

69.

Which of these equations shifts a radical equation right 5 units and down one unit?

a)

$y=\sqrt{x-5}-1$

b)

$y=\sqrt{x+5}-1$

c)

$y=\sqrt{x-5}+1$

d)

$y=\sqrt{x+5}+1$

70.

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

a)

Shifted right 5, shifted down 2, and reflected over the x-axis

b)

Reflected over the x-axis, vertical stretch by 2, and shifted right 5

c)

Reflected over the x-axis, vertical stretch by 2, and shifted left 5

d)

Shifted right 5, shifted down 2

71.

a)

$y=-\sqrt{x+1}$

b)

$y=\sqrt{x+1}$

c)

$y=-\sqrt{x}-1$

d)

$y=\sqrt{x}+1$

72.

Determine the equation for the graph.

a)

$y=2\sqrt{x}-4$

b)

$y=-\sqrt{x-4}$

c)

$y=2\sqrt{x}$

d)

$y=2\sqrt{x}+4$

73.

Match the correct equation with the given graph.

a)

$y=\sqrt{x}+2$

b)

$y=\sqrt{x}-2$

c)

$y=\sqrt{x+2}$

d)

$y=\sqrt{x-2}$

74.

What function best describes this graph?

a)

$y=-\sqrt{x+4}-2$

b)

$y=\sqrt{x-4}-2$

c)

$y=-\sqrt{x-4}-2$

d)

$y=\sqrt{x+4}+2$

75.

What is the domain of this function?

$y=\sqrt{x-1}-3$

a)

{x ∣ x ≥ 1}

b)

{x ∣ x ≤ 1}

c)

{x ∣ x ≥ -3}

d)

{x ∣ x ≥ -1}

76.

What is the range of this function?

$y=\sqrt{x-2}+4$

a)

{f(x) ∣ f(x) ≥ -2}

b)

{f(x) ∣ f(x) ≥ 2}

c)

{f(x) ∣ f(x) ≥ 4}

d)

{f(x) ∣ f(x) ≥ -4}

77.

Which is the graph of the square root parent function?

a)

A

b)

B

c)

C

d)

D

78.

What is the domain of this graph?

a)

x ≥ -1

b)

x ≤ -1

c)

x ≥ 0

d)

x ≤ 0

79.

What is the range of the function in this graph?

a)

y ≤ 3

b)

y ≥ 3

c)

y ≤ 0

d)

y ≥ 0

80.

$y=\sqrt{x+5}$

a)

b)

c)

d)

81.

Identify the Transformations.

a)

Vertical stretch by 2 and down 4

b)

Horizontal compression by ½ and down 4

c)

Vertical stretch by 2 and up 4

d)

Horizontal compression by ½ and right 4

82.

Which graph represents the function?

a)

b)

c)

d)

83.

What kind of function is represented by the graph?

a)

Cube Root Function

b)

Cubic Function

c)

Polynomial Function

d)

Square Root Function

84.

Which of the facts is not true about the graph shown?

a)

The range is y ∈ ℝ

b)

The function has been shifted 6 units right.

c)

The function has been shifted up 1 unit

d)

The function has been vertically stretched by a factor of 2.

85.

What is the center point of the function?

a)

(5,-1)

b)

(5,1)

c)

(-5,-1)

d)

(-5,1)

86.

What is the Domain of ALL Cube Root Functions?

a)

(−∞,∞)

b)

[0,∞)

c)

(−∞,0]

d)

All Cube Root Functions are different.

87.

Which function matches the graph?

a)

A

f(x) = ∛(x + 3) + 2

b)

B

f(x) = − ∛(x - 3) + 2

c)

C

f(x) = ∛(x - 3) + 2

d)

D

f(x) = ∛(x - 2) + 3

88.

Identify the parameter changes on the parent functions.

a)

Vertical stretch by 2 and down 4

b)

Horizontal compression by ½ and down 4

c)

Vertical stretch by 2 and up 4

d)

Horizontal compression by ½ and right 4

89.

What is the Range for the graph?

a)

A

2 ≤ y < ∞

b)

B

− ∞ < y ≤ 3

c)

C

3 ≤ y < ∞

d)

D

− ∞ < y < ∞

90.

a)

x = 49

b)

x = 53

c)

x = 45

d)

x = 18

91.

Solve the square root equation:

a)

A

b)

B

c)

C

d)

D

92.

Match the equation with the graph

a)

y = √(x-1) - 1

b)

y = √(x+1) - 1

c)

y = √(x-1) + 1

d)

y = √(x+1) + 1

93.

Solve the cube root equation

a)

344

b)

21

c)

-344

d)

-21

94.

Solve the cube root equation

a)

-984

b)

984

c)

26

d)

-26

95.

Solve and check your solution(s).

a)

x = -2

b)

x = -2, 3

c)

x = -2, -3

d)

x = -3

96.

Solve for x; identify extraneous solutions (if any).

a)

x = 4

b)

x = - 4

c)

x = 1

d)

no solution; x = - 4 is extraneous

97.

Solve for x; identify extraneous solutions (if any).

a)

x = 17

b)

x = 5

c)

x = 3

d)

no solution; x = 5 is extraneous

98.

Solve for x:
7 + x^3/2 = 71

a)

2

b)

4

c)

16

d)

8

99.

Solve the Rational Exponent Equation:

a)

A

b)

B

c)

C

d)

D

100.

Solve the radical equation. Don't forget to check your answers!

a)

x = -6

b)

x = 3

c)

x = 7/3

d)

x = -5

101.

Solve and check your solution(s).

a)

x = 2, 3

b)

x = -2, -3

c)

x = -1, -6

d)

No solution

102.

To undo a square root in an equation, you need to

a)

multiply both sides by 2

b)

square both sides

c)

take the square root of both sides

d)

divide both sides by 2

103.

When finding the inverse of a relation,
1st you replace f(x) with y
2nd switch the x's and y's
What do you do next?

a)

solve for y

b)

replace y with f^-1(x)

c)

solve for x

d)

find the greatest common factor

104.

The inverse has been reflected over which line?

a)

y = x

b)

y =1

c)

y = 0

d)

y = x + 1

105.

Find the inverse of
f(x) = 1/4x - 7

a)

f^-1(x) = 1/4x + 7/4

b)

f^-1(x) = -4x + 28

c)

f^-1(x) = -4x - 7

d)

f^-1(x) = 4x + 28

106.

Given that f(x) = 3x + 5 and g(x) = 1/3x + 5, find f(g(x)). Are the two functions inverses of each other?

a)

x + 20 ; Yes they are inverses

b)

x + 20 ; No, they are not inverses

c)

x ; Yes they are inverses

d)

x ; No, they are not inverses

107.

Is the inverse function found correctly?

a)

yes

b)

no

108.

What does an inverse function do?

a)

Nothing

b)

Makes it bigger

c)

Does the opposite of the original function

109.

What operation allows us to verify if functions are inverses?

a)

Multiplying

b)

Dividing

c)

Adding

d)

Composing

110.

a)

Inverse Functions

b)

Not Inverse Functions

111.

a)

Inverse Functions

b)

Not Inverse Functions

112.

a)

Inverse Functions

b)

Not Inverse Functions

113.

Was the inverse function found correctly?

a)

no,

b)

yes

114.

The inverse of the function f(x) is written as ...

a)

f ^-1(x)

b)

f ²(x)

c)

f '(x)

d)

f ⁺(x)

115.

Which is f ^-1(x)?

a)

f^-1(x) = 3x + 5

b)

f^-1(x) = 3x - 5

c)

f^-1(x) = 3x - 15

d)

f^-1(x) = 3x + 15

116.

$g\left(x\right)=-7x^5+7$ Find the inverse of the function.

a)

$g^{-1}\left(x\right)=^5\sqrt{\frac{x-7}{7}}$

b)

$g^{-1}\left(x\right)=-^5\sqrt{\frac{x-7}{7}}$

c)

$g^{-1}\left(x\right)=^5\sqrt{-\frac{x-7}{7}}$

d)

$g^{-1}\left(x\right)=-^5\sqrt{\frac{x-7}{7}}$

117.

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

a)

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

b)

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

c)

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

d)

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

118.

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

a)

$\frac{x}{3}$

b)

$\frac{3}{x}$

c)

$0.3x$

d)

$x\times3$

119.

Find the inverse of $f(x)=10+7x$

a)

$f^{-1}(x)=\frac{x-7}{10}$

b)

$f^{-1}(x)=\frac{x-10}{7}$

c)

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

120.

Find the inverse of $f(x)=\frac{x-5}{3}$

a)

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

b)

$f^{-1}(x)=3x+5$

c)

$f^{-1}(x)=5x+3$

121.

Determine the inverse for the function:

S (x) = $\frac{2x^2\ -7}{4}$

a)

S^-1(x) = $\frac{2x-4}{7}$

b)

S^-1(x) = $\frac{4x+7}{2}$

c)

S^-1(x) = $\sqrt[]{\frac{4x+7}{2}}$

d)

S^-1(x) =

$\sqrt[]{\frac{2x+7}{4}}$

122.

Determine the inverse for the function:

P (x) = 2x² + 1

a)

P^-1(x) = $\frac{x^2-1}{2}$

b)

P^-1(x) = $\frac{x^2+1}{2}$

c)

P^-1(x) = $\sqrt[]{\frac{x-1}{2}}$

d)

P^-1(x) = $\sqrt[]{\frac{x+1}{2}}$

123.

Evaluate the composition of functions at the indicated value/number.

a)

20

b)

2

c)

14

d)

17

124.

Evaluate the composition of functions at the indicated value/number.

a)

-29

b)

25

c)

-35

d)

-25

125.

Evaluate the composition of functions at the indicated value/number.

a)

18

b)

13

c)

-24

d)

22

Unit 5 Review

Total questions: 125

Worksheet time: 8hrs 26mins

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