Absolute Value Function and Inequality Graphing

What is the vertex for  $f\left(x\right)=-3\left|x+2\right|+4$  ?

• (-2, -3)

• (2, 4)

• (-2, 4)

• (-6, 4)

• (2, -4)

Describe the transformation for  $f\left(x\right)=-2\left|x+1\right|-3$  

•  $f\left(x\right)$  is  $\left|x\right|$  shrunk vertically by a factor of 2, shifted right 1 and up 3.

•  $f\left(x\right)$  is  $\left|x\right|$  reflected across the x-axis, stretched vertically by a factor of 2, shifted left 1 and down 3.

•  $f\left(x\right)$  is  $\left|x\right|$  reflected across the x-axis, compressed vertically by a factor of 2, shifted left 1 and up 3.

•  $f\left(x\right)$  is  $\left|x\right|$  reflected across the x-axis, stretched vertically by a factor of 2, shifted right 3 and down 1.

What is the equation of the graph?

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

• $f\left(x\right)=-4\left|x+1\right|+4$

• $f\left(x\right)=4\left|x+1\right|+4$

• $f\left(x\right)=4+4\left|x-1\right|$

What is the equation of the graph?

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

• $f\left(x\right)=2\left|x-2\right|-1$

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

• $f\left(x\right)=-2\left|x+2\right|-1$

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

Find the domain and range of the graph.

• $D:\ \left(-\infty,\ \infty\right)$ $R:\ \ \left(-\infty,\ \infty\right)$

• $D:\ \ \left(-\infty,\ \infty\right)\ \ \ R:\ \ \left(-\infty,\ -1\right]$

• $D:\ \ \left(-\infty,\ \infty\right)\ \ \ \ R:\ \ \left[-\infty,\ -1\right)$

• $D:\ \ All\ Real\ Numbers$ $R:\ \ y\ge-1$

• $D:\ \ All\ Real\ Numbers$ $R:\ \ \left[-1,\infty\right)$

 $f\left(x\right)\ge\ 1-\frac{1}{3}\left|x-3\right|$  Select the correct graph that matches.  

• 
• 
• 
• 
• 

Which point is a solution for the graph?

• (3, 1)

• (10, -10)

• (-5, 50)

• (2, 4)

 $y=-10+2\left|x+4\right|$  Describe the transformation of

• Reflected across the x-axis, stretched vertically be a factor of 8 and shifted left 4.

• Reflected across the x-axis, stretched vertically by a factor of 10, shifted left 4 and up 2.

• Stretched vertically by a factor of 2, shifted left 10 and up 4.

• Stretched vertically by a factor of 2, shifted left 4 and down 10.

 $f\left(x\right)=\pm a\left|x-h\right|+k$  What does "a" (just a) do?

• stretches or compresses the graph

• shifts the graph left or right

• moves the graph up or down

• reflects across the x-axis

Tags

CCSS.HSF.BF.B.3

 $f\left(x\right)=\pm a\left|x-h\right|+k$  What does the "-" in front of "a" do to the graph?

• Shifts the graph  left 

• moves the graph down

• reflects the graph across the y-axis

• reflects the graph across the x-axis

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.4