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5.4 Solving absolute value equations and inequalities by graphin

Total questions: 36

Worksheet time: 2hrs 24mins

Name
Class
Date
1.
| x - 2 | > 3
Is this an "and"  or an "or" problem?
a)
and
b)
or
2.
| x - 6 | < 4
Is this an "and"  or an "or" problem?
a)
and
b)
or
3.
What is the correct first step?
a)
divide by 10
b)
multiply by 10
c)
make it two inequalities with an "or"
d)
make it two inequalities with and "and
4.
| 2x + 12 | < 8
Which is the correct first step?
a)
2x + 12 < 8 and 2x+12 >-8
b)
2x + 12 < 8 or 2x+12 >-8
c)
2x + 12 < 8 and 2x+12 <-8
d)
2x + 12 < 8 or 2x+12 >-8
5.
What is the first step? 
a)
Get absolute value alone by subtracting 5 from both sides
b)
Get absolute value alone by dividing by 5 on both sides
c)
Split into two equations
6.
When graphing an inequality, you use an open dot when you use which symbol?
a)
<, >
b)
≤, ≥ 
7.
When you graph an inequality, you used a closed dot when you use which symbols?
a)
≤, ≥ 
b)
<, >
8.

Which compound inequality involves >,≥ when solving absolute value inequalities?

a)

and

b)

or

9.

Which compound inequality involves <, ≤ when solving absolute value inequalities?

a)

and

b)

or

10.

Which graph matches the inequality?

a)
b)
c)
d)
11.

Which graph matches the inequality?

a)
b)
c)
d)
12.

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

a)

Yes

b)

No

13.

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

14.

Which graph matches the function:

y = -2|x - 3| + 5

a)

A

b)

B

c)

C

d)

D

15.

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

a)

Above

b)

Below

16.

Is the line for the inequality

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

a)

Dotted

b)

Solid

17.

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

18.

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

19.

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

20.

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)

21.

An absolute value equation can have which numbers of solutions?

(select all that apply)

a)

No Solution

b)

1 Solution

c)

2 Solutions

d)

4 Solutions

22.

The graphs here represent the two sides of an absolute value equation. How many solutions does the equation have?

a)

No solutions

b)

1 solution

c)

2 solutions

23.

The graphs here represent the two sides of an absolute value equation. How many solutions does the equation have?

a)

No solutions

b)

1 solution

c)

2 solutions

24.

For an absolute value equation to have ONE solution, which of the following should be true?

a)

|__| = +#

b)

|__| = -#

c)

|__| = 0

25.

For an absolute value equation to have TWO solution, which of the following should be true?

a)

|__| = +#

b)

|__| = -#

c)

|__| = 0

26.

For an absolute value equation to have NO solution, which of the following should be true?

a)

|__| = +#

b)

|__| = -#

c)

|__| = 0

27.

Solve the absolute value equation:

∣x∣=6\left|x\right|=6  

a)

1 solution: x=6

b)

2 solutions: x=-6,6

c)

1 solution: x=-6

d)

none of the above

28.

Solve the absolute value equation:

∣2x+1∣=5\left|2x+1\right|=5  

a)

2 solutions: x=2,-3

b)

1 solution: x=3

c)

1 solution: x=2

d)

none of the above

29.

Solve the absolute value equation:

−2∣3x−1∣=4-2\left|3x-1\right|=4  

a)

2 solutions: x=-1,1

b)

1 solution: x=1/3

c)

no solution

d)

none of the above

30.

Select the absolute value equation:

3∣x−4∣−3=03\left|x-4\right|-3=0  

a)

no solution

b)

1 solution: x=4

c)

2 solutions: x=3,5

31.

Solve the absolute value equation:

2∣x+2∣−5=−52\left|x+2\right|-5=-5  

a)

1 Solution: x=-2

b)

2 solutions: x=-12,8

c)

no solution

d)

none of the above

32.

Which graph matches the inequality?

a)
b)
c)
d)
33.

What is the vertex of

y≥−∣x−2∣+3y\ge-\left|x-2\right|+3  

a)

(2,3)\left(2,3\right)  

b)

(−2,3)\left(-2,3\right)  

c)

(3,−2)\left(3,-2\right)  

d)

(3,2)\left(3,2\right)  

34.

Is the line for the inequality

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

a)

Dotted

b)

Solid

35.

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

a)

Above

b)

Below

36.

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)

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