Shifting & Scaling Absolute Value Graphs

What does k represent? Choose all that apply.

• left/right shift

• up/down shift

• horizontal shift

• vertical shift

What does h represent? Choose all that apply.

• left/right shift

• up/down shift

• horizontal shift

• vertical shift

What is the definition of absolute value?

• The distance a number is to zero

• A positive number

• A number that has a value with a different sign

 Complete the description of the transformation. $g\left(x\right)=\left|x-1\right|+9$ 

• up by 9 unit and right by 1 units

• down by 1 unit and right by 9 units

• up by 9 unit and left by 1 units

• down by 1 unit and left by 9 units

 Complete the description of the transformation. $g\left(x\right)=\left|x-4\right|-4$ 

• down by 4 unit and left by 4 units

• up by 4 unit and right by 4 units

• down by 4 unit and right by 4 units

What is the equation for g(x)?

• $g\left(x\right)=\left|x-3\right|$

• $g\left(x\right)=\left|x+3\right|$

• $g\left(x\right)=\left|x\right|-3$

• $g\left(x\right)=\left|x\right|+3$

What is the equation for g(x)?

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

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

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

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

The graph of y=|x| is shifted down by 6 units and to the left by 9 units.

What is the equation of the new graph?

• $y=\left|x-9\right|-6$

• $y=\left|x+9\right|+6$

• $y=\left|x+9\right|-6$

• $y=\left|x-9\right|+6$

The graph of y=|x| is shifted up by 4 units and to the right by 5 units.

What is the equation of the new graph?

•  $y=\left|x+5\right|+4$ 

•  $y=\left|x+4\right|+5$ 

•  $y=\left|x+4\right|-5$ 

•  $y=\left|x-5\right|+4$ 

The graph of y = |x| is scaled vertically by a factor of  $\ \frac{1}{3}$ .

•  $y=\left|x\right|-3$  

•  $y=-3\left|x\right|$  

•  $y=\frac{1}{3}\left|x\right|$  

•  $y=\left|x\right|-\frac{1}{3}$