# GRAPHING ABSOLUTE VALUE FUNCTIONS WORKSHEET

Graphing Absolute Value Functions Worksheet :

Worksheet given in this section will be much useful for the students who would like to practice problems on graphing absolute value functions.

Before look at the worksheet, if you would like to learn, how to graph an absolute value function,

## Graphing Absolute Value Functions Worksheet - Problems

Problem 1 :

Graph the absolute value function given below.

y  =  |x - 1|

Problem 2 :

Graph the absolute value function given below.

y  =  |x - 1| - 2

Problem 3 :

Graph the absolute value function given below.

y  =  |x + 3| + 3

Problem 4 :

Graph the absolute value function given below.

y  =  |x - 2|

Problem 5 :

Graph the absolute value function given below.

y  =  |x + 4| + 3

Problem 6 :

Graph the absolute value function given below.

y  =  |x - 4| - 4

Problem 7 :

Graph the absolute value function given below.

y  =  -|x - 2| - 2

Problem 8 :

Graph the absolute value function given below.

y  =  -|x - 4|

Problem 9 :

Graph the absolute value function given below.

y  =  -|x| + 2

Problem 10 :

Graph the absolute value function given below.

y  =  -|x + 1| + 3

Problem 11 :

Graph the absolute value function given below.

y  =  -|x| + 4

Problem 12 :

Graph the absolute value function given below.

y  =  -|x + 1| - 1 ## Graphing Absolute Value Functions Worksheet - Solutions

Problem 1 :

Graph the absolute value function given below.

y  =  |x - 1|

Solution :

The given absolute value function is in the form :

y - k  =  |x - h|

That is,

y  =  |x - 1|

To get the vertex, equate (x - 1) and y to zero.

x - 1  =  0  and  y  =  0

x  =  1  and  y  =  0

Therefore,  the vertex is

(1, 0)

So, the graph of the given absolute value function is Problem 2 :

Graph the absolute value function given below.

y  =  |x - 1| - 2

Solution :

Write the given absolute value function in the form :

y - h  =  |x - h|

That is,

y  =  |x - 1| - 2

y + 2  =  |x - 1|

To get the vertex, equate (x - 1) and (y + 2) to zero.

x - 1  =  0  and  y + 2  =  0

x  =  1  and  y  =  -2

Therefore, the vertex is

(1, -2)

So, the graph of the given absolute value function is Problem 3 :

Graph the absolute value function given below.

y  =  |x + 3| + 3

Solution :

Write the given absolute value function in the form :

y - h  =  |x - h|

That is,

y  =  |x + 3| + 3

Subtract 3 from each side.

y - 3  =  |x + 3|

To get the vertex, equate (x + 3) and (y - 3) to zero.

x + 3  =  0  and  y - 3  =  0

x  =  -3  and  y  =  3

Therefore, the vertex is

(-3, 3)

So, the graph of the given absolute value function is Problem 4 :

Graph the absolute value function given below.

y  =  |x - 2|

Solution :

The given absolute value function is in the form :

y - k  =  |x - h|

That is,

y  =  |x - 2|

To get the vertex, equate (x - 2) and y to zero.

x - 2  =  0  and  y  =  0

x  =  2  and  y  =  0

Therefore, the vertex is

(2, 0)

So, the graph of the given absolute value function is Problem 5 :

Graph the absolute value function given below.

y  =  |x + 4| + 3

Solution :

Write the given absolute value function in the form :

y - h  =  |x - h|

That is,

y  =  |x + 4| + 3

Subtract 3 from each side.

y - 3  =  |x + 4|

To get the vertex, equate (x + 4) and (y - 3) to zero.

x + 4  =  0  and  y - 3  =  0

x  =  -4  and  y  =  3

Therefore, the vertex is

(-4, 3)

So, the graph of the given absolute value function is Problem 6 :

Graph the absolute value function given below.

y  =  |x - 4| - 4

Solution :

Write the given absolute value function in the form :

y - h  =  |x -h|

That is,

y  =  |x - 4| - 4

y + 4  =  |x - 4|

To get the vertex, equate (x - 4) and (y + 4) to zero.

x - 4  =  0  and  y + 4  =  0

x  =  4  and y  =  -4

Therefore, the vertex is

(4, -4)

So, the graph of the given absolute value function is Problem 7 :

Graph the absolute value function given below.

y  =  -|x - 2| - 2

Solution :

Write the given absolute value function in the form

y - h  =  |x - h|

That is,

y  =  -|x - 2| - 2

y + 2  =  -|x - 2|

To get the vertex, equate (x - 2) and (y + 2) to zero.

x - 2  =  0  and  y + 2  =  0

x  =  2  and  y  =  -2

Therefore, the vertex is

(2, -2)

Because there is negative sign in front of the absolute sign, we have to flip the curve over.

So, the graph of the given absolute value function is Problem 8 :

Graph the absolute value function given below.

y  =  -|x - 4|

Solution :

The given function is in the form :

y - k  =  |x - h|

That is,

y  =  -|x - 4|

To get the vertex, equate (x - 4) and y to zero.

x - 4  = 0  and  y  =  0

x  =  4  and  y  =  0

Therefore, the vertex is

(4, 0)

Because there is negative sign in front of the absolute sign, we have to flip the curve over.

So, the graph of the given absolute value function is Problem 9 :

Graph the absolute value function given below.

y  =  -|x| + 2

Solution :

Write the given absolute value function in the form :

y - h  =  |x - h|

That is,

y  =  -|x| + 2

Subtract 2 from each side.

y - 2  =  -|x|

To get the vertex, equate x and (y - 2) to zero.

x  = 0  and  y - 2  =  0

x  =  0  and  y  =  2

Therefore, the vertex is

(0, 2)

Because there is negative sign in front of the absolute sign, we have to flip the curve over.

Hence, the graph of the given absolute value function is Problem 10 :

Graph the absolute value function given below.

y  =  -|x + 1| + 3

Solution :

Write the given absolute value function in the form :

y - h  =  |x - h|

That is,

y  =  -|x + 1| + 3

Subtract 3 from each side.

y - 3  =  -|x + 1|

To get the vertex, equate (x + 1) and (y - 3) to zero.

x + 1  =  0  and  y - 3  =  0

x  =  -1  and  y  =  3

Therefore, the vertex is

(-1, 3)

Because there is negative sign in front of the absolute sign, we have to flip the curve over.

So, the graph of the given absolute value function is Problem 11 :

Graph the absolute value function given below.

y  =  -|x| + 4

Solution :

Write the given absolute value function in the form

y - h  =  |x - h|

That is,

y  =  -|x| + 4

Subtract 4 from each side.

y - 4  =  -|x|

To get the vertex, equate x and (y - 4) to zero.

x  =  0  and  y - 4  =  0

x  =  0  and  y  =  4

Therefore, the vertex is

(0, 4)

Because there is negative sign in front of the absolute sign, we have to flip the curve over.

So, the graph of the given absolute value function is Problem 12 :

Graph the absolute value function given below.

y  =  -|x + 1| - 1

Solution :

Write the given absolute value function in the form :

y - h  =  |x - h|

That is,

y  =  -|x + 1| - 1

y + 1  =  -|x + 1|

To get the vertex, equate (x + 1) and (y + 1) to zero.

x + 1  =  0  and  y + 1  =  0

x  =  -1  and  y  =  -1

Therefore, the vertex is

(-1, -1)

Because there is negative sign in front of the absolute sign, we have to flip the curve over.

So, the graph of the given absolute value function is  After having gone through the stuff given above, we hope that the students would have understood, how to graph absolute value function.

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