1.1 1.2 Linear Functions & Transformations

Identify the function family to which g belongs. Compare the graph of the function to the graph of its parent function.

• Quadratic; translations 2 units down

• Absolute Value; translation 2 units down and 1 unit left

• Quadratic; translation 2 units down and 1 left

• Absolute Value; translation 2 units down

Write an equation of the new function g.

 $f\left(x\right)=2x+1$  ; translation 3 units up

•  $g\left(x\right)=2x+7$  

•  $g\left(x\right)=2x-2$  

•  $g\left(x\right)=2x+4$  

•  $g\left(x\right)=2x-5$  

Write an equation of the new function g.

 $f\left(x\right)=-3\left|x-4\right|$  ; vertical shrink by a factor of  $\frac{1}{2}$  

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

•  $g\left(x\right)=-6\left|x-4\right|$  

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

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

Write an equation of the new function g.  $f\left(x\right)=-2x+1$  ; vertical stretch by a factor of 3

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

•  $g\left(x\right)=-6x+1$  

•  $g\left(x\right)=-6x+3$  

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

 Write an equation of the new function g.

 $f\left(x\right)=3\left|x+5\right|$  ; reflection in the x-axis

•  $g\left(x\right)=-3\left|x+5\right|$  

•  $g\left(x\right)=3\left|-x+5\right|$  

•  $g\left(x\right)=3\left|-x-5\right|$  

•  $g\left(x\right)=3\left|x-5\right|$  

 Write an equation of the new function g.

 $f\left(x\right)=2x-5$  ; translation 4 units left

•  $g\left(x\right)=2x-9$  

•  $g\left(x\right)=2x-1$  

•  $g\left(x\right)=2x-13$  

•  $g\left(x\right)=2x+3$  

Write an equation of the new function g.  $f\left(x\right)=2x-4$  ; horizontal stretch by a factor of 2

•  $g\left(x\right)=4x-4$  

•  $g\left(x\right)=x-2$  

•  $g\left(x\right)=x-4$  

•  $g\left(x\right)=4x-8$  

Write an equation of the new function g. $f\left(x\right)=\left|x-2\right|+1$  ; translation 3 units right

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

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

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

•  $f\left(x\right)=\left|x-5\right|+1$  

Write an equation of the new function g.  $f\left(x\right)=2\left|x+2\right|-3$  ; reflection in the y-axis

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

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

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

Write an equation of the new function g.  $f\left(x\right)=\left|2x+4\right|$  ; horizontal shrink by a factor of  $\frac{1}{3}$  

•  $g\left(x\right)=\left|6x+24\right|$  

•  $g\left(x\right)=\left|6x+4\right|$  

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

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