Absolute Value Functions & Inequalities

The graph of

 $f\left(x\right)=\left|x\right|$  is reflected about the x-axis and translated 2 units left. What is the equation of the new graph?

•  $f\left(x\right)=\left|x+2\right|$  

•  $f\left(x\right)=-\left|x+2\right|$  

•  $f\left(x\right)=-\left|x-2\right|$  

•  $f\left(x\right)=-\left|x\right|-2$  

Tags

CCSS.HSF.BF.B.3

The graph of

 $f\left(x\right)=\left|x\right|$  is stretched by a factor of 3 and translated 2 right and 4 up. What is the equation of the new graph?

•  $f\left(x\right)=3\left|x-2\right|+4$  

•  $f\left(x\right)=3\left|x+2\right|-4$  

•  $f\left(x\right)=\frac{1}{3}\left|x-2\right|+4$  

•  $f\left(x\right)=-3\left|x+2\right|-4$  

Tags

CCSS.HSF.BF.B.3

What is the vertex of

 $f\left(x\right)=-\frac{2}{3}\left|x-1\right|-6$  ?

• (-1, -6)

• (1, -6)

• (-1, 6)

• (1, 6)

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

What is the axis of symmetry of 

 $f\left(x\right)=-\frac{2}{3}\left|x-1\right|-6$  ?

• y = 1

• y = -1

• x = -1

• x = 1

What is the inequality for the graph?

• $y>\left|x+2\right|-3$

• $y\ge\left|x-2\right|+3$

• $y<\left|x+2\right|-3$

• $y\le\left|x+2\right|-3$

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.REI.D.11

CCSS.HSA.REI.D.12

What is the inequality for the graph?

• $y\ge\frac{1}{2}\left|x+3\right|+1$

• $y\ge\frac{1}{2}\left|x-3\right|+1$

• $y\le2\left|x+3\right|+1$

• $y\ge2\left|x-3\right|+1$

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.D.12

What is the equation of the graph?

• $f\left(x\right)=-\left|x+2\right|+6$

• $f\left(x\right)=\left|x-2\right|+6$

• $f\left(x\right)=-\left|x+2\right|-6$

• $f\left(x\right)=-\left|x-2\right|+6$

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

What is the vertex of the graph of

 $f\left(x\right)=-\left|x-2\right|+6$  ?

• (2, 6)

• (-2, 6)

• (-2, -6)

• (2, -6)

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

What is the axis of symmetry of

 $f\left(x\right)=-\left|x-2\right|+6?$  

• x = -2

• y = -2

• x = 2

• y = 2

What are the intercepts of

 $f\left(x\right)=-\left|x-2\right|+6?$  

• (-4, 0), (8, 0)

• 4, 8, -4

• 4

• (0, 4), (8, 0), (-4, 0)

Tags

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11