Transformations of Functions

Which expression represents a translation 7 units to the right?

• $f\left(x\right)+7$

• $f\left(x+7\right)$

• $f\left(x\right)-7$

• $f\left(x-7\right)$

What happens to a graph after a vertical stretch?

• It becomes narrower

• It becomes wider

Which expression represents a reflection over the x-axis?

• $f\left(-x\right)$

• $-f\left(x\right)$

Match the equation

 $y=\left(x-2\right)^2+2$  to its description

• Translation right 2 and up 2

• Translation right 2 and down 2

• Translation left 2 and up 2

• Translation left 2 and down 2

Which expression represents a vertical compression?

•  $3\sqrt{x}$  

•  $\sqrt{3x}$  

•  $\frac{1}{3}\sqrt{x}$  

•  $\sqrt{\frac{1}{3}x}$  

If the blue graph is

 $f\left(x\right)=x^2$ , the red graph must be...

•  $f\left(x+3\right)=\left(x+3\right)^2$  

•  $f\left(x-3\right)=\left(x-3\right)^2$  

•  $f\left(x\right)+3=x^2+3$  

•  $f\left(x\right)-3=x^2-3$  

Which expression represents a vertical stretch?

• $af\left(x\right);\ \ a>1$

• $af\left(x\right);\ \ 0<a<1$

Which equation represents a transformation of  $f\left(x\right)$  onto  $g\left(x\right)$  

•  $g\left(x\right)=2f\left(x\right)$  

•  $g\left(x\right)=\frac{1}{2}f\left(x\right)$  

•  $f\left(x\right)=2g\left(x\right)$  

•  $f\left(x\right)=\frac{1}{2}g\left(x\right)$  

Describe the transformation  $-\sqrt{x}$  

• reflection over the x-axis

• reflection over the y-axis

Which equation represents the graphed function?

• $-\left|x-1\right|+3$

• $\left|x-1\right|+3$

• $\left|-x-1\right|+3$

• $\left|x-1\right|-3$