Practice: Absolute Value Characteristics

What is the domain of the absolute value function?

• $-\infty<x<\infty$

• $-\infty\le x\le\infty$
  

• $4\le x<\infty$

• $4<x<\infty$

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

What is the range of the absolute value function?

•  $-\infty<y<\infty$  

•  $-\infty<y\le4$  

•  $0<y<\infty$  

•  $4\le y<\infty$  
  

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

What is the vertex of the absolute value function?

• $\left(4,0\right)$

• $(0,4)$
  

• $\left(-\infty,\infty\right)$

• $\left[4,\infty\right]$

Tags

CCSS.HSF-IF.C.7D

What is the range?

 $y=-\frac{1}{3}\left|x-5\right|+6$  

•  $\left[6,\infty\right)$ 

•  $\left(-\infty,6\right]$  

•  $\left(-\infty,5\right]$  

•  $\left[5,\infty\right)$  

Tags

CCSS.HSF-IF.C.7D

What is the vertex?

 $f\left(x\right)=-\frac{1}{3}\left|x-2\right|+7$  

•  $\left(2,7\right)$  
  

•  $\left(-2,7\right)$  

•  $\left[-2,7\right]$  

•  $\left[2,7\right]$  

Tags

CCSS.HSF-IF.C.7D

What is the range of the following function:

 $f\left(x\right)=-\frac{1}{2}\left|x+2\right|-3$  

•  $\left(-\infty,\ -2\right]$  

•  $\left[-2,\ \infty\right)$  

•  $\left(-\infty,\ -3\right]$  

•  $\left[-3,\ \infty\right)$  

•  $\left(-\infty,\ \infty\right)$  

 $y=-2\left|x\right|-11$  

What is the end behavior as  $x\rightarrow-\infty$ 

•  $y\rightarrow\infty$  
  

•  $y\rightarrow-\infty$  
  

•  $y\rightarrow0$  

•  $y\rightarrow-11$  

Tags

CCSS.HSF-IF.C.7D

Which interval is the function increasing?

 $f\left(x\right)=-\left|x-3\right|+4$  

•  $\left(-\infty,\ 4\right)$  

•  $\left(4,\ \infty\right)$  

•  $\left(3,\ \infty\right)$  

•  $\left(-\infty,\ 3\right)$  

Tags

CCSS.HSF-IF.C.7D

Which interval is the function decreasing?

 $f\left(x\right)=-\left|x-3\right|+4$  

•  $\left(-\infty,\ 4\right)$  

•  $\left(4,\ \infty\right)$  

•  $\left(3,\ \infty\right)$  

•  $\left(-\infty,\ 3\right)$  

Tags

CCSS.HSF-IF.C.7D

What is the range?

• $\left(-\infty,\infty\right)$

• $\left[1,\infty\right)$

• $\left(-\infty,1\right]$

• $\left[2,\infty\right)$

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5