Free Printable Unit 4-Rational Functions Study Guide

1.

Simplify the radical expression:
$\sqrt{128a^3b^4}$

a)

$8ab^2\sqrt{2a}$

b)

$2a\sqrt{8ab^2}$

c)

$2ab\sqrt{64ab}$

d)

$64ab^2\sqrt{2a}$

2.

Simplify the radical expression:
$\sqrt{27m^7p^{4\ }}$

a)

$3m\sqrt{3m^3p^2}$

b)

$3m^3p^2\sqrt{3m}$

c)

$9mp\sqrt{3m}$

d)

$9m^3p^2\sqrt{3m}$

3.

Simplify the radical expression:
$\sqrt{92a^2b^3}$

a)

$23ab\sqrt{2b}$

b)

$2ab\sqrt{23b}$

c)

$4ab\sqrt{23b}$

d)

$4a^2b^2\sqrt{23b}$

4.

Simplify the radical:

\sqrt{25x^6}

a)

$5x$

b)

$25x^3$

c)

$5x^3$

d)

$5x^4$

5.

Write as a radical expression
y²⁄ ³

a)

2y³

b)

√y³

c)

∛y²

d)

3y²

6.

Write with rational exponents:√(7x)

a)

(7x)^½

b)

7x^½

c)

7x²

d)

(7x)²

7.

a)

b)

c)

d)

8.

Simplify the following expression:
³√125x⁶y¹⁸

a)

25x²y⁶

b)

-5x³y¹⁵

c)

5x²y⁶

d)

25x³y¹⁵

9.

Multiply then simplify the radicals.

a)

$\sqrt{24x^5y^6}$

b)

$4x^5y^6\sqrt{3}$

c)

$2x^2y^3\sqrt{6x}$

10.

a)

0

b)

3∛1

c)

3∛7

d)

3

11.

a)

-5√1

b)

8√2 + 13√3

c)

21√5

d)

20√5

12.

a)

17√2

b)

9√1

c)

9

d)

9√2

13.

$\sqrt{x}+4=0$

(a)

14.

$5=-2\sqrt{x-1}+15$

(a)

15.

$3\sqrt{x-1}-9=0$

(a)

16.

$16=7\sqrt[3]{6x+28}+30$

(a)

17.

$5\sqrt[3]{2x+1}=25$

(a)

18.

$-3=4\sqrt[3]{10x-3}+9$

(a)

19.

$x=\sqrt{9x-20}$

(a)

20.

Which function matches the graph?

a)

A

f(x) = √(x - 4) - 2

b)

B

f(x) = √(x + 2) - 4

c)

C

f(x) = √(x - 2) - 4

d)

D

f(x) = √(x + 4) - 2

21.

What is the Range for the graph?

a)

A

-4 ≤ y < ∞

b)

B

− ∞ < y ≤ -2

c)

C

-2 ≤ y < ∞

d)

D

− ∞ < y ≤ -4

22.

What is the Domain for the graph?

a)

A

-4 ≤ x < ∞

b)

B

− ∞ < x ≤ -2

c)

C

-2 ≤ x < ∞

d)

D

− ∞ < x ≤ -4

23.

Which function matches the graph?

a)

A

f(x) = √(x - 1) + 3

b)

B

f(x) = − √(x + 1) + 3

c)

C

f(x) = √(-x + 1) + 3

d)

D

f(x) = − √(x + 3) − 1

24.

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

25.

What is the Range for the graph?

a)

A

2 ≤ y < ∞

b)

B

− ∞ < y ≤ 3

c)

C

3 ≤ y < ∞

d)

D

− ∞ < y < ∞

26.

Which is the graph of the square root parent function?

a)

A

b)

B

c)

C

d)

D

27.

What is the DOMAIN?

a)

[0, ∞)

b)

(-∞, 0)

c)

All real numbers

d)

{0, 1, 2, 3, 4,...}

28.

What is the range of this function?

a)

[-4,∞)

b)

[0, ∞)

c)

(-∞, 4]

d)

(0,∞)

29.

What is the x-intercept of this function?

a)

(3,2)

b)

(2,3)

c)

(0,11)

d)

(11,0)

30.

What is the y-intercept of the graph?

a)

(-1,0)

b)

(0,-1)

c)

(0,3)

d)

(3,0)

31.

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

a)

18

b)

$5+\sqrt{7}$

c)

$5-\sqrt{7}$

d)

32

32.

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

a)

$16-\sqrt{2}$

b)

$4-\sqrt{2}$

c)

14

d)

18

33.

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)

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

34.

Rationalize the denominator:
$\frac{\sqrt{4}}{\sqrt{121}}$

a)

$\frac{4}{11}$

b)

$\frac{\sqrt{484}}{121}$

c)

$\frac{2}{11}$

d)

$\frac{2\sqrt{121}}{121}$

35.

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)

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

36.

Write in exponential form
∛x⁷

a)

x⁷∕ ³

b)

x3⁄7

c)

3x⁷

d)

7x³

37.

Write as a radical expression
y²⁄ ³

a)

2y³

b)

√y³

c)

∛y²

d)

3y²

38.

Write as a radical expression
y¹⁄ ³

a)

∛y

b)

y³

c)

√y

d)

1∕ 3y

39.

Write with rational exponents:√(7x)

a)

(7x)^½

b)

7x^½

c)

7x²

d)

(7x)²

40.

Write the above expression in exponential form.

a)

b)

c)

d)

41.

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

a)

1

b)

2

c)

3

d)

4

42.

Write the expression in exponential form:
√23

a)

23^1/2

b)

23^-1/2

c)

23²

d)

23^-2

43.

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

a)

add

b)

subtract

c)

multiply

d)

divide

44.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

45.

x⁻⁶

a)

1 ⁄ x⁶

b)

x⁶

c)

-x⁶

d)

-1 ⁄ x⁶

46.

Simplify.

(2n⁴ )( 5n⁴⁾

a)

7n⁴

b)

10n¹⁶

c)

10n⁸

d)

none of the above

47.

Simplify.

a)

a⁸b¹³

b)

a²b⁷

c)

a¹⁵b³⁰

d)

none of the above

48.

Simplify the expression with positive exponents

a)

b)

c)

d)

49.

simplify the expression (5³x²y⁴)⁰

a)

5xy

b)

1

c)

0

d)

5

50.

Simplify $\left(2a^4b^6c^{-2}\right)^3$ . Your answer should not have any negative exponents.

a)

$6a^{12}b^{18}c^{-6}$

b)

$8a^{12}b^{18}c^6$

c)

$\frac{8a^{12}b^{18}}{c^6}$

d)

$8a^7b^9c$

51.

$\left(\frac{1}{2}\right)^2\ \times\left(\frac{1}{2}\right)^3$

a)

$\left(\frac{1}{2}\right)^6$

b)

$\left(\frac{1}{2}\right)^5$

c)

$\left(\frac{1}{2}\right)^1$

52.

$yx^{\frac{1}{3}}\cdot xy^{\frac{3}{2}}$

a)

$x^{\frac{4}{3}}y^{\frac{5}{2}}$

b)

$x^{\frac{2}{3}}y^{\frac{1}{2}}$

c)

$x^{\frac{1}{3}}y^{\frac{3}{2}}$

d)

$x^{\frac{2}{3}}y^{\frac{4}{3}}$

53.

Simplify . Your answer should contain only positive exponents. $4v^{\frac{2}{3}}\cdot v^{-1}$

a)

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

b)

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

c)

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

d)

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

54.

a)

y¹⁶

b)

y³

c)

16y

d)

y⁴⁸

55.

Billy was asked to solve 3⁵∙3⁴. He got 9²⁰. What error did he make?

a)

When he multiplies exponents, he is supposed to add the base and the exponent

b)

When he multiplies exponents, he is supposed to multiply the base and keep the exponents

c)

When he multiplies exponents, he is supposed to keep the base and add the exponents if the base is the same

d)

None of the above

56.

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

a)

f ^-1(x)

b)

f ²(x)

c)

f '(x)

d)

f ⁺(x)

57.

The inverse has been reflected over which line?

a)

y = x

b)

x = 0

c)

y = 0

d)

x = -y

58.

Which of the following is NOT TRUE about inverse functions?

a)

Inverse functions are reflections of each other over the line y = x.

b)

You find the inverse by switching x and y in the equation.

c)

The domain of a function always becomes the domain of its inverse.

d)

The domain of a function always becomes the range of its inverse.

59.

What are the missing values if g(x)=f^-1(x)?

a)

(9,-5)

b)

(-9,-5)

c)

(5,9)

d)

(-9,5)

60.

What is the best description?

a)

They are both functions, but not inverse functions.

b)

They are inverse functions.

c)

They are reflected over y=x, but they are not both functions.

d)

They are not reflected over y=x, and they are not both functions.

61.

f(x) = -4x - 12

What is f^-1(x)?

a)

f^-1(x) = 4x - 3

b)

$f^{-1}\left(x\right)=-\frac{1}{4}x-3$

c)

$f^{-1}\left(x\right)=\frac{1}{4}x+3$

d)

f^-1(x) = -4x - 3

62.

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

63.

What is the inverse of the points (1,3)(2,4)(6,2)?

a)

(2,6)(3,1)(4,2)

b)

(-3,-1)(-4,-2)(-2,-6)

c)

(1,3)(2,4)(6,2)

d)

(-1,-3)(-2,-4)(-6,-2)

64.

Find the inverse.

f(x)=2x-2

a)

f^-1(x)=1/2x+1

b)

f^-1(x)=-2-1/2x

c)

f^-1(x)=-7/3x-20/3

d)

2-2/5x

65.

What does it mean to find the inverse of a function?

a)

switch the x's and y's

b)

divide the x's and y's by 2

c)

make the x's and y's negative

d)

make the x's and y's the same

Unit 4-Rational Functions Study Guide

Total questions: 65

Worksheet time: 2hrs 18mins

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