Free Printable Absolute Value Equations and Inequalities Test

1.

$\left|x+10\right|=11$

a)

3, -3

b)

4, -4

c)

1, -21

d)

0, -2

2.

$\left|-3x-6\right|=15$

a)

$-7$

b)

$-7,\ 3$

c)

$\frac{26}{3},\ -10$

d)

$-\frac{20}{3},\ 4$

3.

$\left|4+2x\right|-1=19$

a)

$-\frac{8}{7}$

b)

$8,\ -12$

c)

$no\ solution$

d)

$\frac{1}{5},\ -\frac{8}{5}$

4.

$10\left|2x-1\right|+9=59$

a)

$\frac{5}{3},\ 5$

b)

$-\frac{4}{5},\ 1$

c)

$\frac{12}{5},\ -2$

d)

$3,\ -2$

5.

$\left|10x+1\right|=41$

a)

$4,\ -\frac{21}{5}$

b)

$\frac{52}{5},\ -10$

c)

$\frac{5}{2},\ -2$

d)

$\frac{21}{5},\ -3$

6.

$\left|x-1\right|+2=10$

a)

$6,\ -6$

b)

$9,\ -7$

c)

$-5,\ 5$

d)

$13,\ 5$

7.

$\left|4x-2\right|+10=16$

a)

$\frac{13}{3},\ -3$

b)

$2$

c)

$2,\ -1$

d)

$\frac{2}{3}$

8.

$-10+\left|2x+9\right|=-13$

a)

$-\frac{1}{2}$

b)

$-5$

c)

$-5,\ 13$

d)

$no\ solution$

9.

$9-2\left|4x-2\right|=-3$

a)

$2,\ 0$

b)

$2,\ -1$

c)

$1$

d)

$1,\ \frac{17}{3}$

10.

$9+\left|8x+8\right|=33$

a)

$7,\ -10$

b)

$\frac{8}{5},\ -\frac{12}{5}$

c)

$2,\ -4$

d)

$\frac{12}{7},\ -2$

11.

What's a way to define absolute value?

a)

The value of a number

b)

The opposite of a number

c)

The distance of a number from zero

d)

The multiplicative inverse of a number

12.

What is the reason that absolute value is always written as a positive?

a)

Absolute value is talking about numbers so it must be positive.

b)

Absolute value does not always have to be positive.

c)

Absolute value is like a clock it has only positive numbers.

d)

Absolute value is talking about distance, distance is always measured by positive numbers.

13.

What is the absolute value of |-26|.

a)

26

b)

-26

c)

0

d)

-20

14.

What is the absolute value of |572|.

a)

275

b)

-572

c)

57

d)

572

15.

Which has the same absolute value as -55?

a)

0

b)

-1

c)

1

d)

55

16.

Boston has a temperature of -20 degrees. It is colder in New York than in Boston. Select the value that could represent the temperature of New York

a)

0

b)

30

c)

-30

d)

-19

17.

Evaluate the expression.
|1 - 5|

a)

4

b)

-4

c)

-6

d)

6

18.

Evaluate the expression.
|5 + 4|

a)

9

b)

-9

c)

-1

d)

1

19.

Evaluate the expression.
|-2| + |-5|

a)

7

b)

-7

c)

3

d)

-3

20.

|x-3|=40

a)

x = 43, x = -37

b)

x = 43, x = -43

c)

x = -43, x = 37

d)

x = 43

21.

|x+7|=12

a)

x = -5, x = 19

b)

x = 5, x = -19

c)

x = 5, x = -5

d)

x = 12, x = -7

22.

|v + 8| − 5 = 2

a)

{-1,-15}

b)

{-1,-5}

c)

{-15,15}

d)

No Solution

23.

|-2 - 4n| = 34

a)

n = -9, n = 8

b)

n = 9, n = 8

c)

n = -9

d)

n = 8

24.

|2a - 10| = 6

a)

a = 8, a = 5

b)

a = 2

c)

a = 8

d)

a = 8, a = 2

25.

3| −8x| + 8 = 80

a)

{-7/3, 7/3}

b)

{-3,3}

c)

{11/3,-11/3}

d)

No Solution

26.

8|-2x + 4| = 96

a)

x = -4, x = 8

b)

x = -4

c)

x = -4, x = -8

d)

x = 4, x = 8

27.

-|−2r − 1| = 11

a)

{-6,5}

b)

{5,-6}

c)

-6

d)

No Solution

28.

a)

2, -6

b)

0, 6

c)

2, -2

d)

6, -1

29.

a)

0, 10

b)

5, -5

c)

-10, 5

d)

0

30.

a)

-5

b)

5, -5

c)

0

31.

Describe the movements.

y= −|x|+4

a)

Left 4, Down 1

b)

Reflect over x-axis, Down 4

c)

Reflect over x-axis, Up 4

d)

Right 4, Up 1

32.

Which graph matches the function:

y = -2|x - 3| + 5

a)

A

b)

B

c)

C

d)

D

33.

Is this graph correct for y= -2|x+4|

a)

Yes

b)

No

34.

What is the correct equation for this graph?

a)

y < |x+4| -3

b)

y ≤ |x+4|+ 3

c)

y ≤ |x-4| -1

d)

y < 1/2|x+4| + 1/2

35.

What is the correct equation for this graph?

a)

y > -|x| + 7/2

b)

y > -2|x| + 4

c)

y > -1/2|x| + 2

d)

y > |x| + 4

36.

What is the correct equation for this graph?

a)

y ≤ 2|x-1| - 1

b)

y ≤ 1/2|x-1| + 4

c)

y ≥ -2|x+1| - 2

d)

y ≥ -2|x-1| + 1

37.

Which graph matches the inequality?

a)

b)

c)

d)

38.

Which graph matches the inequality?

a)

b)

c)

d)

39.

Which graph matches the inequality?

a)

b)

c)

d)

40.

Is the line for the inequality

f(x) ≥|x+3|- 9 going to solid or dotted?

a)

Dotted

b)

Solid

41.

Are we going to shade above or below for f(x) ≤|x|+1?

a)

Above

b)

Below

42.

What is the vertex of the following function?

y=2|x-3|+1

a)

(2,3)

b)

(-3,1)

c)

(2,-3)

d)

(3,1)

43.

Which is the equation for the following graph?

a)

f(x) = 2|x - 1| + 1

b)

f(x) = 2 $\left|x+1\right|-1$

c)

f(x) = $2\left|x-1\right|-1$

d)

f(x) = $2\left|x+1\right|+1$

44.

a)

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

b)

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

c)

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

d)

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

45.

a)

$f\left(x\right)=\frac{3}{2}\left|x\right|+2$

b)

$f\left(x\right)=\frac{3}{2}\left|x+2\right|$

c)

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

d)

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

46.

a)

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

b)

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

c)

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

d)

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

47.

a)

$f\left(x\right)=\left|x-1\right|$

b)

$f\left(x\right)=2\left|x-1\right|$

c)

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

d)

$f\left(x\right)=-\left|x-1\right|$

48.

a)

$f\left(x\right)=\left|x-1\right|$

b)

$f\left(x\right)=\left|x\right|$

c)

$f\left(x\right)=-\left|x\right|$

d)

$f\left(x\right)=-x$

49.

a)

$f\left(x\right)=\left|x+2\right|-3$

b)

$f\left(x\right)=\frac{4}{3}\left|x+2\right|-3$

c)

$f\left(x\right)=\frac{3}{4}\left|x+2\right|-3$

d)

$f\left(x\right)=\frac{4}{3}\left|x+3\right|-2$

50.

a)

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

b)

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

c)

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

d)

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

51.

a)

$f\left(x\right)=-2\left|x-1\right|-1$

b)

$f\left(x\right)=-2\left|x+1\right|-1$

c)

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

d)

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

52.

a)

$f\left(x\right)=2\left|x-2\right|-2$

b)

$f\left(x\right)=2\left|x+2\right|-2$

c)

$f\left(x\right)=2\left|x-2\right|+2$

d)

Ooh! Pick this one! Pick this one!

53.

a)

$f\left(x\right)=\left|x+3\right|+3$

b)

$f\left(x\right)=-\left|x-3\right|+3$

c)

$f\left(x\right)=-\left|x+3\right|+3$

d)

No, really! This time pick this one! I promise this is the one!

54.

If the "a" value is greater than (>) 1, what kind of transformation will happen?

a)

The graph will stretch or get skinnier

b)

The graph will compress or flatten

c)

reflection across the x-axis

d)

The graph will shift left or right

55.

If the "a" value is less than (<) 1 and greater than (<) 0, what kind of transformation will happen?

a)

The graph will stretch or get skinner

b)

The graph will compress or flatten

c)

reflection across the x-axis

d)

The graph will shift to the left or the right

56.

If the "a" value is less than (<) 0, what kind of transformation will happen?

a)

vertical stretch by a factor of 1

b)

vertical compress by a factor of 1

c)

reflection across the x-axis

d)

horizontal shift to the right

57.

If you add "h" what will happen to the graph?

a)

The graph will stretch or get skinnier

b)

horizontal shift to the left "h" units

c)

reflection across the x-axis

d)

horizontal shift to the right by "h" units

58.

If the "k" value is positive, what kind of transformation will happen?

a)

The graph will stretch or get skinnier

b)

horizontal shift to the left "k" units

c)

vertical shift up by "k" units

d)

horizontal shift to the right by "k" units

59.

If the "k" value is negative, what kind of transformation will happen?

a)

vertical shift down by "k" units

b)

horizontal shift to the left "k" units

c)

vertical shift up by "k" units

d)

horizontal shift to the right by "k" units

60.

Which of the following graphs represents an absolute value function?

a)

b)

c)

d)

61.

Which of the following graphs represents the function $y\ =\ \left|x+1\right|$ ?

a)

b)

c)

d)

62.

Which of the following graphs represents the function $y\ =\ \left|x\right|+2$ ?

a)

b)

c)

d)

63.

Which of the following graphs represents the function $y\ =\ \left|x-2\right|-4$ ?

a)

b)

c)

d)

64.

What is the vertex of the absolute value graph $y\ =\ \left|x+1\right|+3$ ?

(a)

65.

Label the VERTEX of the graph given.

A

B

C

D

66.

Choose the correct equation for the graph.

a)

$y=\left|x+2\right|$

b)

$y=\left|x-2\right|$

c)

$y=\left|x\right|+2$

d)

$y=\left|x\right|-2$

67.

Choose the correct equation for the graph.

a)

$y=\left|x+2\right|$

b)

$y=\left|x-2\right|$

c)

$y=\left|x\right|+2$

d)

$y=\left|x\right|-2$

68.

Choose the correct equation for the graph.

a)

$y=\left|x+2\right|$

b)

$y=\left|x-2\right|$

c)

$y=\left|x\right|+2$

d)

$y=\left|x\right|-2$

69.

Choose the correct equation for the graph.

a)

$y=\left|x+2\right|$

b)

$y=\left|x-2\right|$

c)

$y=\left|x\right|+2$

d)

$y=\left|x\right|-2$

70.

Choose the correct equation for the graph.

a)

$y=\left|x\right|$

b)

$y=\left|-x\right|$

c)

$y=-\left|x\right|$

d)

$y=\left|x+4\right|$

71.

If the "a" value is greater than (>) 1, what kind of transformation will happen?

a)

The graph will stretch or get skinnier

b)

The graph will compress or flatten

c)

reflection across the x-axis

d)

The graph will shift left or right

72.

If the "a" value is less than (<) 1 and greater than (<) 0, what kind of transformation will happen?

a)

The graph will stretch or get skinner

b)

The graph will compress or flatten

c)

reflection across the x-axis

d)

The graph will shift to the left or the right

73.

If the "a" value is less than (<) 0, what kind of transformation will happen?

a)

vertical stretch by a factor of 1

b)

vertical compress by a factor of 1

c)

reflection across the x-axis

d)

horizontal shift to the right

74.

If you subtract "h" what will happen to the graph?

a)

vertical stretch by a factor of 1

b)

vertical compress by a factor of 1

c)

reflection across the x-axis

d)

horizontal shift to the right by "h" units

75.

If you add "h" what will happen to the graph?

a)

The graph will stretch or get skinnier

b)

horizontal shift to the left "h" units

c)

reflection across the x-axis

d)

horizontal shift to the right by "h" units

76.

If the "k" value is positive, what kind of transformation will happen?

a)

The graph will stretch or get skinnier

b)

horizontal shift to the left "k" units

c)

vertical shift up by "k" units

d)

horizontal shift to the right by "k" units

77.

If the "k" value is negative, what kind of transformation will happen?

a)

vertical shift down by "k" units

b)

horizontal shift to the left "k" units

c)

vertical shift up by "k" units

d)

horizontal shift to the right by "k" units

78.

Which of the following graphs represents the function $y\ =\ \left|x\right|+2$ ?

a)

b)

c)

d)

79.

Which of the following graphs represents the function $y\ =\ \left|x-2\right|-4$ ?

a)

b)

c)

d)

80.

What is the vertex of the absolute value graph $y\ =\ \left|x+1\right|+3$ ?

(a)

81.

Label the VERTEX of the graph given.

A

B

C

D

82.

Choose the correct equation for the graph.

a)

$y=\left|x+2\right|$

b)

$y=\left|x-2\right|$

c)

$y=\left|x\right|+2$

d)

$y=\left|x\right|-2$

83.

Choose the correct equation for the graph.

a)

$y=\left|x+2\right|$

b)

$y=\left|x-2\right|$

c)

$y=\left|x\right|+2$

d)

$y=\left|x\right|-2$

84.

Choose the correct equation for the graph.

a)

$y=\left|x+2\right|$

b)

$y=\left|x-2\right|$

c)

$y=\left|x\right|+2$

d)

$y=\left|x\right|-2$

85.

Choose the correct equation for the graph.

a)

$y=\left|x+2\right|$

b)

$y=\left|x-2\right|$

c)

$y=\left|x\right|+2$

d)

$y=\left|x\right|-2$

86.

Choose the correct equation for the graph.

a)

$y=\left|x\right|$

b)

$y=\left|-x\right|$

c)

$y=-\left|x\right|$

d)

$y=\left|x+4\right|$

Absolute Value Equations and Inequalities Test

Total questions: 86

Worksheet time: 3hrs 52mins

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