Introduction to Graphing Absolute Value Inequalities

Introduction to Graphing Absolute Value Inequalities

Poll

Current Mood?

Multiple Choice

Let's think back to Unit 1 and Identifying Parent Functions.

What shape does the Absolute Value graph have?

• V shape

• U shape

• Squiggle (like a chromosome)

• eyebrow shape

Multiple Choice

Which of the following is the parent function for Absolute Value?

• $y=\left|x\right|$

• $y=\log\ x$

• $y=x^2$

• $y=\sqrt{x}$

Multiple Choice

 $y=a\left|x-h\right|+k$  

Remember transformations?

Given  $y=\left|x-3\right|+2$ , describe the transformation.

• Moves right 3 and down 2

• Moves right 3 and up 2

• Moves left 3 and down 2

• Moves left 3 and up 2

Multiple Choice

 $y=a\left|x-h\right|+k$  

Remember transformations?

Given  $y=\left|x+7\right|-4$ , describe the transformation.

• Moves right 7 and down 4

• Moves right 7 and up 4

• Moves left 7 and down 4

• Moves left 7 and up 4

Multiple Select

 $y=a\left|x-h\right|+k$  

Remember transformations?

Given  $y=-\left|x-7\right|+2$ , describe the transformation.
Check all that apply.

• Flips down

• Moves right 7

• Moves left 7

• Moves up 2

• Moves down 2

Multiple Choice

Determine the domain of the graph:

• $x\ \epsilon\ \left(-\infty,\ +\infty\right)$

• $x\ \epsilon\ \left[5,\ +\infty\right)$

• $x\ \epsilon\ \left[-2,\ +\infty\right)$

• $x\ \epsilon\ \left(-\infty,\ 5\right]$

Multiple Choice

Determine the range of the graph:

•  $y\ \epsilon\ \left(-\infty,\ +\infty\right)$ 

•  $y\ \epsilon\ \left[5,\ +\infty\right)$ 

•  $y\ \epsilon\ \left[-2,\ +\infty\right)$ 

•  $y\ \epsilon\ \left(-\infty,\ 5\right]$ 

Multiple Choice

Determine the domain of the graph:

• $x\ \epsilon\ \left(-\infty,\ +\infty\right)$

•  $x\ \epsilon\ \left[6,\ +\infty\right)$ 

• $x\ \epsilon\ \left[-2,\ +\infty\right)$

•  $x\ \epsilon\ \left(-\infty,\ -2\right]$ 

Multiple Choice

Determine the range of the graph:

•  $y\ \epsilon\ \left(-\infty,\ +\infty\right)$ 

•  $y\ \epsilon\ \left[6,\ +\infty\right)$ 

•  $y\ \epsilon\ \left[-2,\ +\infty\right)$ 

•  $y\ \epsilon\ \left(-\infty,\ -2\right]$ 

Multiple Choice

What extrema exist for the graph shown?

• No extrema exist for this graph

• (-2, -4)

• (-4, -2)

• (0, -2)

Today's Topic

Graphing Absolute Value Inequalities on the Coordinate Plane

Multiple Choice

Here is a sample problem:
Which of the following represents the graph for this inequality?

 $y<\left|x-6\right|-3$  

Multiple Choice

Try again:
Which of the following represents the graph for this inequality?

 $y<\left|x+6\right|+3$  

Know your Transformation Rules

Sometimes that is all you need to get the question correct.

But what about this next one?

Multiple Choice

Which of the following represents the graph of the inequality shown?

 $y\ge\left|x-2\right|-4$  


What is your guess?

Here is What you Need to Know

• SOLID lines for  $\le\ and\ \ge$   

• DOTTED lines for  $<\ and\ >$  

• Shade ABOVE for  $>\ and\ \ge$  (greater thans)

• Shade BELOW for  $<\ and\ \le$  (less thans)

Multiple Select

Which of the following describes the graph of the inequality shown?

 $y<\left|x-2\right|-4$  


Select all that apply.

• dotted line

• solid line

• shade above

• shade below

Multiple Choice

Which of the following represents the graph of the inequality shown?

 $y<\left|x-2\right|-4$  

Multiple Select

Which of the following describes the graph of the inequality shown?

 $y\ge-\left|x+7\right|-1$  


Select all that apply.

• dotted line

• solid line

• shade above

• shade below

Multiple Choice

Which of the following represents the graph of the inequality shown?

 $y\ge-\left|x-7\right|+1$  

Multiple Choice

Which of the following inequalities represents the following graph?

• $y>\left|x\right|+3$

• $y>-\left|x\right|+3$

• $y<-\left|x\right|+3$

• $y<\left|x\right|+3$

Multiple Choice

Which of the following inequalities represents the following graph?

•  $y\le-\left|x+2\right|$ 

•  $y\le-\left|x-2\right|$ 

•  $y<-\left|x+2\right|$ 

•  $y<-\left|x-2\right|$ 

Desmos

• You can type in an inequality and desmos will do the graphing for you.

• But often, you can get the right answer by looking at dotted/solid and if it is shaded above or below.