Introduction to Graphing Absolute Value Inequalities

V shape

U shape

Squiggle (like a chromosome)

eyebrow shape

$y=\left|x\right|$

$y=\log\ x$

$y=x^2$

$y=\sqrt{x}$

Moves right 3 and down 2

Moves right 3 and up 2

Moves left 3 and down 2

Moves left 3 and up 2

Moves right 7 and down 4

Moves right 7 and up 4

Moves left 7 and down 4

Moves left 7 and up 4

Flips down

Moves right 7

Moves left 7

Moves up 2

Moves down 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

No extrema exist for this graph

(-2, -4)

(-4, -2)

(0, -2)

dotted line

solid line

shade above

shade below

dotted line

solid line

shade above

shade below

$y>\left|x\right|+3$

$y>-\left|x\right|+3$

$y<-\left|x\right|+3$

$y<\left|x\right|+3$

 $y\le-\left|x+2\right|$ 

 $y\le-\left|x-2\right|$ 

 $y<-\left|x+2\right|$ 

 $y<-\left|x-2\right|$