Free Printable Alg 2 Ch. 5 Test Review

1.

(5³x²y⁴)⁰

a)

5xy

b)

1

c)

0

d)

5

2.

a)

x⁴y⁶

b)

1/(x⁴y⁶)

c)

y

d)

1

3.

(ab⁸c)(a^-17c¹⁰)

a)

a¹⁷b⁸c¹¹

b)

a¹⁶b⁸c¹¹

c)

(b⁸c¹¹)/(a¹⁶)

d)

a^-17b⁸c¹⁰

4.

Simplify:
(x + 4) - (x² + 3x - 1)

a)

-x² - 2x + 5

b)

x² + 4x + 3

c)

x² + 4x + 5

d)

-x² - 2x + 3

5.

Simplify:
(x² - 3x - 2) + (5x² + 10x - 5)

a)

5x⁴ - 30x² + 10

b)

6x² + 7x - 7

c)

6x⁴+ 7x² - 7

d)

4x² + 13x + 7

6.

Simplify:
(2x - 2)(x² + 3x + 5)

a)

3x² - 10

b)

6x² - 10

c)

x² + 5x + 3

d)

2x³ + 4x² + 4x - 10

7.

Find the value of the polynomial when x = 4.
x² + 3x - 10

a)

18

b)

9

c)

4

d)

6

8.

factor:
x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

9.

Factor: 8x³ + 1

a)

(2x + 1)(4x² + 2x + 1)

b)

(2x + 1)(4x² - 2x + 1)

c)

(8x + 1)(x² + 1)

d)

(2x - 1)(4x²+ 2x + 1)

10.

Factor p³- 3p² - 16p + 48

a)

p² ( p - 3) (p - 3)

b)

(p² - 16) (p - 3)

c)

(p + 4) (p - 4) (p - 3)

11.

Simplify without zero or negative exponents.

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

a)

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

b)

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

c)

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

d)

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

12.

Write without zero or negative exponents.

\frac{2ef^{-1}}{e^{-1}}

a)

$2f$

b)

$-\frac{2e^2}{f}$

c)

$\frac{2}{f}$

d)

$\frac{2e^2}{f}$

13.

Write in the simplest form without negative or zero exponents.

$\frac{\left(r^{-1}s^{-2}\right)^{-3}}{\left(rs\right)^{-2}}$

a)

$r^5s^8$

b)

$rs^4$

c)

$r^5s^7$

d)

$\frac{1}{r^5s^8}$

14.

Write in simplest form without negative or zero exponents.

$\left(\frac{x}{y^2}\right)^{-1}\ \cdot\ \ \left(\frac{x^{-2}}{y}\right)^2$

a)

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

b)

$x^3$

c)

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

d)

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

15.

Write in simplest form without negative or zero exponents.

$\left(\frac{u}{v^{-1}}\right)^0\left(\frac{u^{-1}}{v^2}\right)^2\frac{\left(uv\right)^{-1}}{\left(u^3v^{-4}\right)^0}$

a)

$-\frac{u^3}{v^6}$

b)

$\frac{v^2}{u^3}$

c)

$\frac{1}{u^3v^6}$

d)

$\frac{u^2}{v^3}$

16.

Simplify.

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

a)

$\frac{x\left(x-2\right)}{\left(x+2\right)}$

b)

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

c)

$\frac{x}{2}$

d)

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

17.

Simplify

$\frac{x^2-9}{x^2+6x+9}$

a)

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

b)

$1$

c)

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

d)

$\left(x-3\right)$

18.

Simplify

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

a)

$\frac{36z}{y^3x}$

b)

$\frac{y^3x}{36z}$

c)

$\frac{y^3x}{12z}$

d)

$\frac{12z}{y^3x}$

19.

Which of the following is correct?

a)

Root over Power

b)

Power over Root

20.

What is the value of (-2)^3?

a)

-8

b)

-6

c)

6

d)

8

21.

Write the following expression in radical form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

22.

Write the following expression in radical form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

23.

Write the following expression in radical form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

24.

Write the following expression in exponential form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

25.

a)

(5x)^-2/1

b)

(5x)^2/1

c)

(5x)^-1/2

d)

(5x)^1/2

26.

a)

m^{- 2}

b)

m^{- 0.5}

c)

m^1/2

d)

m^0.5

27.

$\left(4xy^3\right)^3$

a)

$x^3y^9$

b)

$64x^3y^9$

c)

$12x^4y^6$

d)

$64x^4y^6$

28.

Simplify:
(5ab²)²

a)

25a²b⁴

b)

10a²b⁴

c)

5a²b⁴

d)

25ab²

29.

a)

2

b)

-2

c)

4

d)

-4

30.

Question 3

a)

20

b)

11

c)

4

d)

-2

31.

Solve the equation:

a)

x = 13

b)

x = -23

c)

x = 31

d)

x = 347

32.

What is the inverse of the given coordinates: (1, 2) (3, 8) (-3, 6)

a)

(1, 2) (3, 8) (-3, 6)

b)

(1, 2) (8, 3) (-3, 6)

c)

(-1, -2) (-3, -8) (3, -6)

d)

(2, 1) (8, 3) (6, -3)

33.

When creating an inverse you must...

a)

Switch the x and y

b)

Solve for x

c)

Draw a graph

d)

Potato

34.

Find the inverse of $f\left(x\right)=3x+2$

a)

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

b)

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

c)

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

d)

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

35.

Find the inverse of $f\left(x\right)=-5x-7$

a)

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

b)

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

c)

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

d)

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

36.

Find the inverse of $f\left(x\right)=x^2-4$

a)

$f^{-1}\left(x\right)=\sqrt{x+16}$

b)

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

c)

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

d)

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

37.

Given f(x) = 3x + 10 and g(x) = x - 2

Find f(g(5))

a)

19

b)

23

c)

-10

d)

None of these.

38.

What is f(g(3))?

a)

1/8

b)

8

c)

1/4

d)

1/2

39.

Given f(x) = 2x and g(x) = x²+3 , find f(g(x)).

a)

x²+2x+3

b)

4x²+3

c)

2x²+3

d)

2x²+6

40.

The composition of any function, f(x), and its inverse, f^-1(x) =

a)

x

b)

f(x)

c)

1

d)

0

41.

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.

42.

What's the best description?

a)

They are both functions, but not inverse functions.

b)

They are inverses of each other, but they are not both functions.

c)

They are not inverses, and they are not both functions.

d)

They are inverse functions.

43.

Which graph represents f^-1(x) over the same domain?

a)

b)

c)

d)

44.

f(x) = -4x - 12

What is f^-1(x)?

a)

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

b)

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

c)

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

d)

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

45.

Tell how the function transformed from y =x²
y = -2x²

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

46.

What is the equation of this graph?

a)

f(x) = -(x + 1)² + 3

b)

f(x) = -(x - 1)² + 3

c)

f(x) = -(x + 1)² - 3

d)

f(x) = -(x + 1)² - 3

47.

The blue is f(x)=|x|, red must be

a)

g(x)=|x+2|

b)

g(x)=|x|+2

c)

g(x)=|x-2|

d)

g(x)=|x|-2

48.

What is the line of symmetry for the graph shown?

a)

$x=1$

b)

$y=1$

c)

$x=-2$

d)

$y=0$

49.

Find the inverse of

y=\frac{1}{2+3x}

.

a)

$y=\frac{1}{3x}-\frac{2}{3}$

b)

$y=\frac{1}{3x}-2$

c)

$y=2-3x$

d)

$y=\frac{2x-1}{3}$

50.

Which of the following statements is NOT true?

a)

The domain of $y=\frac{1}{x}$ is all real numbers except zero.

b)

The range of any exponential function is all real numbers greater than zero.

c)

The domain of $y=x^2$ is the same as the domain of $y=\left|x\right|$

d)

The domain of $y=\sqrt{x}$ is all real numbers except zero

51.

Simplify √-23

a)

-√23

b)

23i

c)

23

d)

i√23

52.

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

53.

When f(x) = x²- 9

and g(x) = x + 3 ,

find f(x) / g(x).

a)

x - 3

b)

x + 3

c)

x - 12

d)

x - 6

54.

f(x)= 4x-7
g(x)= 6x-8
Find f(x)+g(x)

a)

2x+15

b)

10x-15

c)

-2x-15

d)

10x+1

55.

Find the inverse of f(x) = -4x - 12

a)

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

b)

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

c)

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

d)

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

56.

Write as a radical.

a)

a

b)

b

c)

c

d)

d

57.

Write as a rational exponent.

a)

a

b)

b

c)

c

d)

d

58.

Describe the transformations of the following function.

a)

Reflect, Right 2, Up 1

b)

Reflect, Left 2, Up 1

c)

Left 2, Up 1

d)

Reflect, Stretch by 2, Left 2, Up 1

59.

Are the following inverses of each other?

a)

True

b)

False

60.

Find the inverse of f(x) = x² - 5

a)

f^-1(x) = √(x) + 5

b)

f^-1(x) = ∛(x-5)

c)

f^-1(x) =√(x+5)

d)

f^-1(x) = x² - 5

61.

Question 6. Solve.

a)

-5

b)

5

c)

10

d)

25

62.

Solve the equation.

a)

n = 27

b)

n = 18

c)

n = -18

d)

n = 36

63.

Name the parent function.

a)

cube root

b)

quadratic

c)

cubic

d)

square root

e)

linear

64.

Which of the following is the function shown in the graph?

a)

f(x)= -√(x+4) -2

b)

f(x)= √(x-4) -2

c)

f(x)= -√(x-4) -2

d)

f(x)= √(x+4) +2

65.

What is the domain of the function in this graph?

a)

x ≤ 3

b)

x ≥ 3

c)

x ≤ 0

d)

x ≥ 0

66.

What is the range of the function in this graph?

a)

y ≤ 3

b)

y ≥ 3

c)

y ≤ 0

d)

y ≥ 0

67.

Name the parent function.

a)

cube root

b)

quadratic

c)

cubic

d)

square root

e)

linear

68.

Which of the following is the domain shown in the graph?

a)

[4,∞)

b)

[-4,∞)

c)

(4,8)

d)

[-4,8]

69.

What is the standard form of the number 10³?

a)

100

b)

300

c)

1,000

d)

3,000

70.

What is the exponential form of the number 10,000?

a)

10³

b)

10⁴

c)

10⁵

d)

10⁶

71.

What is 60 x 10³?

a)

60,000

b)

.060

c)

6,000

d)

.0060

72.

Simplify the polynomial!

\left(3x^2y^{-3}\right)\left(-2x^3y^5\right)

a)

$6x^{-1}y^2$

b)

$-6x^5y^2$

c)

$xy^{-2}$

d)

$-6x^6y^{-15}$

73.

Simplify the polynomial!

\left(\frac{p^2r^3}{pr^4}\right)^2

a)

$p^4r^4$

b)

$p^3r^2$

c)

$\frac{p^2}{r^2}$

d)

$\frac{p^6}{r^4}$

74.

Describe the end behavior of the function shown

a)

$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty;\ As\ x\rightarrow+\infty,\ f\left(x\right)\rightarrow+\infty$

b)

$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow+\infty;\ As\ x\rightarrow+\infty,\ f\left(x\right)\rightarrow-\infty$

c)

$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow+\infty;\ As\ x\rightarrow+\infty,\ f\left(x\right)\rightarrow+\infty$

d)

$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty;\ As\ x\rightarrow+\infty,\ f\left(x\right)\rightarrow-\infty$

75.

Find p(3) if

$p\left(x\right)=\frac{2}{3}x^3+\frac{1}{3}x^2-5x$

a)

36

b)

30

c)

11

d)

6

76.

What are the x coordinates of the max and min shown here?

a)

x = 0 and 2

b)

x = -1.5 and 2

c)

x = 0 and 1

d)

x = -1.5 and -1

77.

How many real zeros does this graph have?

a)

5 real zeros

b)

2 real zeros

c)

4 real zeros

d)

3 real zeros

78.

Factor

8x^3-27

a)

$\left(8x-3\right)\left(8x^2+24x+9\right)$

b)

$\left(2x-3\right)\left(4x^2+6x+9\right)$

c)

$\left(x-3\right)\left(x^2-3x-9\right)$

d)

prime

79.

What is the degree of this function?

4x^6+7x^2-11x^3

(a)

80.

10(h+1)-4=76

a)

h=10

b)

h=4

c)

h=7

d)

h=76

81.

a)

7

b)

-16

c)

4

d)

-15

82.

What is the inverse of the points
(1,3)(2,4)(6,8)

a)

(3,1)(4,2)(8,6)

b)

(-3,-1)(-4,-2)(-8,-6)

c)

(1,3)(2,4)(6,8)

d)

(-1,-3)(-2,-4)(-6,-8)

83.

What is the inverse of the function
f(x) = 2x + 4 ?

a)

f^-1(x) = 4(x -2)

b)

f^-1(x) = (x-4)/2

c)

f^-1(x) = x/2 - 4

d)

f^-1(x) = x/4 + 2

84.

Find the inverse of f(x) = 5/11x +10

a)

f^-1(x) = 11/5x - 22

b)

f^-1(x) = 5/11x - 22

c)

f^-1(x) = 11/5x - 20

d)

None of the above

85.

Find the inverse of
f(x) = -3x + 3

a)

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

b)

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

c)

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

d)

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

86.

f(x) = 3x + 10
g(x) = x - 2
Find f(g(x))

a)

3x² - 2

b)

3x + 8

c)

3x + 4

d)

None of these.

87.

f(x)=x²-4
h(x)=3x+3
f(h(x))

a)

3x²-9

b)

12x²+8x+5

c)

16x²-36x+20

d)

9x²+18x+5

88.

What is the equation for the red function?

a)

g(x)=x³+1

b)

g(x)=x³-1

c)

g(x)=(x-1)³

d)

g(x)=(x+1)³

89.

If f(x) = x³ is changed to f(x) = - (x + 3)³ + 2, how is the graph transformed?

a)

3 units right, 2 units up, reflected across the y-axis

b)

3 units right, 2 units up, reflected across the x-axis

c)

3 units left, 2 units up, reflected across the y-axis

d)

3 units left, 2 units up, reflected across the x-axis

90.

How did the equation shift from the parent function? y = f(x - 4)

a)

Shift right by 4

b)

Shift left by 4

c)

Horizontal Stretch by 4

d)

Vertical Stretch by 4

e)

Shift down by 4

91.

√(8x-16) ≥ 4

a)

[2,4]

b)

[2, +∞]

c)

[4,+∞]

d)

[-2,4]

92.

3 + √(3x+12) ≤ 9

a)

[-4,8]

b)

(- ∞, 8]

c)

[-4,-2]

d)

[4,6]

93.

4√(2x-1) ≥ -4

a)

(-∞,+∞)

b)

[1, +∞)

c)

[½, +∞)

d)

[½,1]

94.

2√(x-6) +1 < 9

a)

[6,10)

b)

(-∞,22)

c)

[6, 22)

d)

(22, +∞)

95.

√(3x-2 )> 13

a)

[⅔, 57)

b)

(57, +∞)

c)

(-∞, ⅔)

d)

[57, + ∞)

96.

√(3x+1) > √(4x-2)

a)

[½, 3)

b)

[½, +∞)

c)

(-∞, 3)

d)

[- ⅓, ½]

97.

∛(x + 1) < 2

a)

[-1, 7)

b)

(- ∞, 7)

c)

[-1, 1)

d)

(7, + ∞)

98.

∛(x + 5) + 6 ≥ 4

a)

[ -13, +∞ )

b)

( -13, + ∞ )

c)

( -13, -5]

d)

( - ∞, -5]

99.

∛(5x +4) - 4 < 0

a)

[12, +∞)

b)

[ -⅘, 12)

c)

( - ∞, - ⅘]

d)

( -∞, 12 )

100.

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

a)

$x\ne5$

b)

$x\ne0$

c)

$x\ge5$

d)

$x\ge0$

101.

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

a)

$x\ge4$

b)

$x\ge3$

c)

$x\ne3$

d)

$x\ne-4$

102.

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

a)

$x\ne2$

b)

$x\ne5$

c)

$x\ge2$

d)

$x\ge5$

103.

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

a)

$x\ge-4$

b)

$x\le4$

c)

$x\ge4$

d)

$x\le-4$

104.

$\frac{\sqrt{x-3}}{x+8}$ Choose the domain for which the function is defined.

a)

$x\ne3\ and\ x\le8$

b)

$x\ne3\ and\ x\ge8$

c)

$x\ne8\ and\ x\ge3$

d)

$x\ne-8\ and\ x\ge3$

105.

$\frac{\sqrt{x+4}}{x-3}$ Choose the domain for which the function is defined.

a)

$x\ne4\ and\ x\ \le3$

b)

$x\ne3\ and\ x\ge4$

c)

$x\ne3\ and\ x\ge-4$

d)

$x\ne-4\ and\ x\ge3$

106.

What are the domain restrictions of $f\left(x\right)=\frac{x+3}{x^2-16}$ ?

a)

$x\ne4,-4$

b)

$x\ne0$

c)

$x\ge16$

d)

$\left(-4,4\right)$

107.

What are the domain restrictions $f\left(x\right)=\frac{3}{x^2+6x+5}$

a)

$x\ne-5,-1$

b)

$x\ne1,5$

c)

$x>5,\ x<1$

d)

$x<-5,\ x>-1$

Alg 2 Ch. 5 Test Review

Total questions: 107

Worksheet time: 3hrs 25mins

Similar Resources on Wayground