Free Printable Radical Functions

1.

What would be the radicand, if the following expression were rewritten in radical form?

5(xy)^5/6

a)

5

b)

x

c)

5/6

d)

xy

2.

What would be the root index, if the following expression were rewritten in radical form?

12x^5/8

a)

12

b)

8

c)

5

d)

x

3.

What is the root index for the square root of 9?

a)

1

b)

2

c)

3

d)

4

4.

Rewrite the expression using a rational exponent.

a)

4xy¹¹

b)

xy⁴⁴

c)

(xy)^11/4

d)

(xy)^4/11

5.

simplify the following..

36^1/2

a)

36

b)

6

c)

9

d)

18

6.

If the rational exponent of an expression is 5/2, what is the exponent when written in radical form?

a)

5/2

b)

5

c)

2

d)

10

7.

Which of the following does not simplify to an integer?

a)

27^2/3

b)

c)

16^1/2

d)

8.

If rewritten with a radical exponent, which of the following would be the base of the expression provided?

a)

6xy

b)

6x

c)

xy

d)

8/3

9.

Simplify the following

a)

4

b)

9

c)

2

d)

3

10.

a)

13

b)

169

c)

21

d)

2197^2/3

11.

What would be the root index if the following expression were written in radical form?

12x^2/3

a)

The implied root index

b)

2

c)

There is no root index..

d)

3

12.

Simplify the given expression.

49^-1/2

a)

7

b)

1/7²

c)

1/49²

d)

1/7

13.

Write the expression in exponential form.

a)

A

b)

B

c)

C

d)

D

14.

a)

a

b)

b

c)

c

d)

d

15.

a)

a

b)

b

c)

c

d)

d

16.

Rewrite in Radical Form.

a)

A

b)

B

c)

C

d)

D

17.

Rewrite in Exponential Form.

a)

A

b)

B

c)

C

d)

D

18.

Rewrite in Exponential Form.

a)

A

b)

B

c)

C

d)

D

19.

Simplify the radical...
√20a²b⁴

a)

2ab²√5

b)

4ab²√5

c)

5ab²√2

d)

2a²b²√5

20.

Simplify
√98b

a)

√98

b)

9√9b

c)

7√2b

d)

7√8b

21.

Simplify

√45n³

a)

3n√5n

b)

4n√8

c)

4n√-8

d)

10√n

22.

√343k⁴

a)

7k²√7

b)

49k²√7

c)

6k²√7

d)

k²√7

23.

5√48x²

a)

10x√3

b)

15x√3

c)

20x√3

d)

25x√3

24.

√36x³y⁴

a)

6y²x√x

b)

3y²√2x

c)

3y√x

d)

6x√3y

25.

The expression $\sqrt{x^{33}}$ is equivalent to

a)

$x^{16}\sqrt{x}$

b)

$x^4\sqrt{x}$

c)

$x^8\sqrt{x}$

d)

$x^2\sqrt{x}$

26.

a)

A

b)

B

c)

C

d)

D

27.

a)

A

b)

B

c)

C

d)

D

28.

a)

x³√x

b)

7x√x²

c)

x⁶√x

d)

√x

29.

a)

y

b)

y²

c)

√y

d)

y√0

30.

Solve the equation. Remember to check for extraneous solutions.

-7+\sqrt{8p}=-3

a)

$p=-5$

b)

$p=2$

c)

$p=9$

d)

$p=-10,\ 9$

31.

Solve the equation. Remember to check for extraneous solutions.

-5=\sqrt{7x+2}-9

a)

$x=-10,\ 8$

b)

$no\ solution$

c)

$x=2$

d)

$x=8$

32.

Solve the equation. Remember to check for extraneous solutions.

-48=-6\sqrt{\frac{x}{10}}

a)

$x=640,\ 9$

b)

$no\ solution$

c)

$x=-2$

d)

$x=640$

33.

Solve the equation. Remember to check for extraneous solutions.

\sqrt{-1-x}=\sqrt{-8-2x}

a)

$x=7$

b)

$x=-7$

c)

$x=-7,\ 7$

d)

$no\ solution$

34.

Solve the equation. Remember to check for extraneous solutions.

\sqrt{2x+11}=\sqrt{x+10}

a)

$x=-1$

b)

$x=1$

c)

$x=-2$

d)

$no\ solution$

35.

Solve the equation. Remember to check for extraneous solutions.

\sqrt{\frac{m}{10}}=\sqrt{2m-171}

a)

$m=9$

b)

$m=2$

c)

$m=90$

d)

$no\ solution$

36.

Solve the equation. Remember to check for extraneous solutions.

\sqrt{-1-2n}=\sqrt{3-n}

a)

$n=-1$

b)

$n=-4$

c)

$n=-5$

d)

$n=4$

37.

Solve the equation. Remember to check for extraneous solutions.

x=\sqrt{-1-2x}

a)

$x=-1,\ 1$

b)

$x=1$

c)

$x=-1$

d)

$no\ solution$

38.

Solve the equation. Remember to check for extraneous solutions.

\sqrt{40-3k}=k

a)

$k=-8$

b)

$k=-8,\ 3$

c)

$k=5$

d)

$k=-8,\ 5$

39.

Solve the equation. Remember to check for extraneous solutions.

n=\sqrt{-21+10n}

a)

$n=3$

b)

$n=7$

c)

$n=3,\ 7$

d)

$no\ solution$

40.

Solve the equation. Remember to check for extraneous solutions.

\sqrt{6-b}=b

a)

$b=2$

b)

$b=-3$

c)

$b=2,\ -3$

d)

$no\ solution$

41.

Solve.

a)

no solution

b)

6

c)

3

d)

4

42.

Solve and check your solution(s).

a)

x = 2, 3

b)

x = -2, -3

c)

x = -1, -6

d)

No solution

43.

a)

x = -6

b)

x = 3

c)

x = -3

d)

x = 5±

44.

Which function represents the given graph?

a)

b)

c)

d)

45.

a)

x = 2

b)

x = 4

c)

x = 7

d)

x = 9

46.

Solve and check your solution(s).

a)

x = 2, 3

b)

x = -2, -3

c)

x = -1, -6

d)

No solution

47.

Adding or subtracting outside of the square root moves the function up and down. Ex. $\sqrt{x}+3$

a)

True

b)

False

48.

Adding or subtracting inside of the square root moves the function left and right. Ex. $\sqrt{x-2}$

a)

True

b)

False

49.

What is the equation for this graph?

a)

$\sqrt{x}-4$

b)

$\sqrt{x}+4$

c)

$\sqrt{x-4}$

d)

$\sqrt{x+4}$

50.

What is the range of this graph? (output values)

a)

(4, infinity)

b)

(infinity, 4)

c)

(-4, 4)

d)

(-infinity, infinity)

51.

What is the equation for this graph?

a)

$\sqrt{x}-2$

b)

$\sqrt{x}+2$

c)

$\sqrt{x-2}$

d)

$\sqrt{x+2}$

52.

What is the equation for this graph?

a)

$\sqrt{x+3}-2$

b)

$\sqrt{x+3}+2$

c)

$\sqrt{x-3}-2$

d)

$\sqrt{x-3}+2$

53.

What is the equation for this graph?

a)

$\sqrt{x+4}-1$

b)

$\sqrt{x+4}+1$

c)

$\sqrt{x-4}-1$

d)

$\sqrt{x-4}+1$

54.

What is the domain for this graph? (input values)

a)

(2, infinity)

b)

(infinity, 2)

c)

(-2, 2)

d)

(-infinity, infinity)

55.

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

56.

What type of function is shown?

a)

cube root

b)

square root

c)

logarithm

d)

exponential

57.

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

58.

Which of these equations shifts a radical equation left 3 times?

a)

y = √(x) + 3

b)

y = √(x) - 3

c)

y = √(x + 3)

d)

y = √(x - 3)

59.

Which equation is shown graphed?

a)

y = 2√(x)

b)

y = −2√(x)

c)

y = −½√(x)

d)

y = ½√(x)

60.

Describe the transformation.

a)

Down 1

b)

Reflect over y-axis

c)

Up 1

d)

Reflect over x-axis

61.

What are the transformations for the graph of
the parent function f(x) = √x to the function above

a)

Vertical Stretch by a factor of 2; translated down 5 units

b)

Shifted right 2 units and down 5 units

c)

Vertical stretch by a factor of 2; translated left 5 units

d)

Vertical stretch by a factor of 2; translated right one unit

62.

Describe the transformation.

a)

Vertical Stretch by 2

b)

Vertical Shrink by ⅓

c)

Horizontal Shrink by ⅓

d)

Horizontal Stretch by 3

63.

Pick the equation that shows a stretch of 2 and a shift up of 3

a)

y=2√(x+3)

b)

y=2√(x)-3

c)

y=3√(x)2

d)

y=2√(x)+3

64.

Pick the equation that shows a reflection over the x-axis, a stretch of 4, a shift left 5, and a shift up 1

a)

y = 4√(x+5)+1

b)

y = - 4√(x+5)+1

c)

y = - 5√(x+4)+1

d)

y = - 4√(x-5)+1

65.

Describe the transformation.

a)

right 5

b)

left 5

c)

up 5

d)

down 5

66.

What is the domain of this graph?¿Cuál es el dominio de esta gráfica?

a)

x ≥ -1

b)

x ≤ -1

c)

x ≥ 0

d)

x ≤ 0

67.

State the domain and range of $h\left(x\right)=\sqrt[]{x-0.5}-6.3$ .

a)

D: $\left[0.5,\infty\right)$

R: $\left[-6.3,\infty\right)$

b)

D: $\left[-0.5,\infty\right)$

R: $\left[-6.3,\infty\right)$

c)

D: $\left[-6.3,\infty\right)$

R: $\left[0.5,\infty\right)$

d)

D: $\left(0.5,\infty\right)$

R: $\left(-6.3,\infty\right)$

68.

Describe the translation of the function $y=2+3\ \sqrt[]{x+1}$ .

a)

left 1 unit, down 2 units, vertical stretch by 3

b)

left 1 unit, up 2 units, vertical stretch by 3

c)

left 1 unit, up 2 units, vertical stretch by 1/3

d)

right 1 unit, up 2 units

69.

What is the domain for:

g(x) = √(x + 5) - 3

a)

A

-3 ≤ x < ∞

b)

B

− ∞ < x ≤ -3

c)

C

-5 ≤ x < ∞

d)

D

− ∞ < x ≤ -5

70.

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

71.

What is the Range for the graph?

a)

A

2 ≤ y < ∞

b)

B

− ∞ < y ≤ 3

c)

C

3 ≤ y < ∞

d)

D

− ∞ < y < ∞

72.

Which function matches the graph?

a)

A

f(x) = − ∛(x + 3) − 1

b)

B

f(x) = − ∛(x - 3) − 1

c)

C

f(x) = ∛(x + 3) − 1

d)

D

f(x) = ∛(x - 1) + 3

73.

If f(x) = ∛(x) is reflected over the x-axis, vertically compressed by a factor of 1/4, and shifted left 9, which equation is correct?

a)

1/4 ∛(x + 9)

b)

1/4 ∛(x - 9)

c)

- 1/4 ∛(x + 9)

d)

- 1/4 ∛(x - 9)

74.

a)

The range is y ≥ 1

b)

It has been reflected over the y-axis

c)

The function has been shifted up 1 unit

d)

The function has been shifted up 2 units

e)

Shifted to the left 6

75.

Identify the function that corresponds with the graph.

a)

$f\left(x\right)=\sqrt[3]{x+2}-5$

b)

$f\left(x\right)=\sqrt[3]{x-5}+2$

c)

$f\left(x\right)\ =\ \sqrt[3]{x+5}+2$

76.

Solve the cube root equation

a)

900

b)

990

c)

0

d)

90

e)

None

77.

Solve the cube root equation

a)

78

b)

-228

c)

228

d)

-78

e)

None

78.

Solve the cube root equation

a)

-984

b)

984

c)

26

d)

-26

e)

None

79.

Solve for x. Identify extraneous solutions, if any.

a)

x = 4; x = - 8 is extraneous

b)

x = - 8; x = 4 is extraneous

c)

x = - 8; x = 4

d)

no solution; x = - 8 and x = 4 are extraneous

80.

Solve for x. Identify extraneous solutions, if any.

a)

x = 4; x = - 8 is extraneous

b)

x = - 8; x = 4 is extraneous

c)

x = - 8; x = 4

d)

no solution; x = - 8 and x = 4 are extraneous

81.

What is the center point of the function?

a)

(5,-1)

b)

(5,1)

c)

(-5,-1)

d)

(-5,1)

82.

What is the center point of the function?

a)

(5,-3)

b)

(5,3)

c)

(-5,-3)

d)

(-5,3)

83.

What is the H-value of the function?

a)

5

b)

-5

c)

-1

d)

1

84.

What is the K-value of the function?

a)

5

b)

-5

c)

-1

d)

1

85.

What is the Domain of ALL Cube Root Functions?

a)

(−∞,∞)

b)

[0,∞)

c)

(−∞,0]

d)

All Cube Root Functions are different.

86.

What is the Range 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.

Which function matches the graph?

a)

A

f(x) = − ∛(x + 3) − 1

b)

B

f(x) = − ∛(x - 3) − 1

c)

C

f(x) = ∛(x + 3) − 1

d)

D

f(x) = ∛(x - 1) + 3

Radical Functions

Total questions: 88

Worksheet time: 5hrs 37mins

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