Absolute Value Functions

Graphing Absolute Value Functions

100

Identify the vertex and slope of the following function and graph it.

y= |x-3|+4

Vertex : (3,4).      Slope: 1

200

Identify the vertex and slope of the following function and graph it.

y=-|x-4|+1

Vertex: (4,1).       Slope: -1

300

Identify the vertex and slope of the following function and graph it.

y=2|x+5|-3

Vertex: (-5,-3).      Slope: 2

400

Identify the vertex and slope of the following function and graph it.

y= 3|x+2|-5

Vertex: (-2,-5)    Slope: 3

500

Identify the vertex and slope of the following function and graph it.

y=-2|x-2|+4

Vertex: (2,4).     Slope: -2

Solving Absolute Value Equations

100

Solve the absolute value equation ALGEBRAICALLY

-5|x-10|-15=0

-5 |x - 10| - 15 = 0

               + 15    +15

  -5 | x - 10| = 15

(-5|x-10|)/-5= 15/-5

|x-10| = -3

No    Solution

200

Solve the absolute value equation by GRAPHING

|x+1|-4=1

x=-6 and x=4

300

Solve the absolute value equation by GRAPHING

-3|x+3|+3=-3

x = -5 and x = -1

400

Solve the absolute value equation ALGEBRAICALLY

2|x-12|+5 = 15

2|x-12|+5 = 15

          -5     -5

   2|x-12| = 10

(2|x-12|)/2=10/2

x-12 = 5                x-12 = -5

 +12   +12                +12    +12

x = 17        and          x = 7   

500

Solve the absolute value equation ALGEBRAICALLY

4-5|10-5x|=-51

Work will be on the board

x=-1/5 and x= 21/5

Absolute Value Transformations

100

Identify all the transformations for the absolute value function.

y = |x| - 4 

Translates down 4 units

200

Identify all the transformations for the absolute value function.

y = |x + 2| + 10

1. Translates left 2 units

2. Translates up 10 units

300

Identify all the transformations for the absolute value function.

y= - 1/2| x - 5| + 8

1. Reflects over x-axis

2. Vertical Compression by a factor of 1/2

3. Translates right 5 units

4. Translates up 8 units

400

Identify all the transformations for the absolute value function.

y = 3 | x + 3| - 2

1. Vertical stretch by a factor of 3

2. Reflects over y-axis

3. Translates left 3 units

4. Translates down 2 units

500

Identify all the transformations for the absolute value function.

y= -5|x+6|-11

1. Reflects over x-axis

2. Vertical Stretch by a factor of 5

3. Horizontal Stretch by a factor of 2 

4. Translates left 6 units

5. Translates down 11 units