Absolute Value Functions and Equations Review

Review: Graphing Absolute Value Functions

 $y=a\left|x-h\right|+k$  

• a - slope. If a is negative, the function is reflected

• (-h,k) - vertex; h is ALWAYS opposite

Parent Function

•  $y=\left|x\right|$  

• Slope is 1

• Vertex is at (0,0)

• Function opens up

 $y=-\left|x-3\right|$  

• What is the slope?

• What is the vertex?

• Does it open up or open down?

 $y=\left|x+3\right|-3$  

• What is the slope?

• What is the vertex?

• Does it open up or open down?

 $y=-\left|x+6\right|-3$   

• What is the slope?

• What is the vertex?

• Does it open up or open down?

Multiple Choice

Which of the following equations matches the graph?

• $$y=\left|x-3\right|+2$$

• $$y=-\left|x-3\right|+2$$

• $$y=\left|x+3\right|+2$$

• $$y=\left|x+3\right|-2$$

Multiple Choice

$$y=-\frac{1}{2}\left|x\right|+2$$  Which of the following graphs matches the equation

Multiple Choice

Which graph matches the equation?