Absolute Value Functions

Graphing Absolute Value Functions

100

Graph it.

y= |x-3|+4

Vertex : (3,4).      Slope: 1

200

Graph it.

y=-|x-4|+1

Vertex: (4,1).       Slope: -1

300

Graph it.

y=2|x+5|-3

Vertex: (-5,-3).      Slope: 2

400

Graph it.

y= 3|x+2|-5

Vertex: (-2,-5)    Slope: 3

500

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

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

x = 17        and          x = 7   

500

Solve the absolute value equation ALGEBRAICALLY

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

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

Solving Absolute Value Inequalities

100

Solve the absolute value inequality by GRAPHING

|x-2|+3<7

-2 < x< 6

(-2,6)

200

Solve the absolute value inequality ALGEBRAICALLY

|x+4|-22 > -18

   x > 0             or            x < -8

(\-infty,-8)U(0,\infty)

300

Solve the absolute value inequality by GRAPHING

2|x+3|-3>=5

x <=-7 or x>=1

(-\infty,-7)U(1,\infty)

400

Solve the absolute value inequality ALGEBRAICALLY

5|7x-7|+8<=43

0<= x <= 2

[0,2]

500

Solve the absolute value inequality ALGEBRAICALLY

-3|1+2x|+2> -43

-8<x<7

(-8,7)

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|1/2(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

inequalities

100

k / 7 > 1 or

 -7 + k <= -10

k > 7 or k <= -3

(-\infty,-3]U(7,\infty)

200

-1 < x / 7 < 0

-7 < x < 0

300

4x + 7 >= 27 

or

9 + 2x <= 3

x >= 5 or x <= -3

(\-infty,,-3]U[5,\infty)

400

-32 <= 3 + 7k < 73

-5 <= k < 10

[-5,10)

500

3x - 8 >= 4 - 3x

or

4x - 7 >= 9 + 8x

x >= 2 or x <= -4

(-\infty, -4]U[2,\infty)