Transformation Review

Transform  $f\left(x\right)=x^2$ by vertical stretch by a factor of 3 and translate up 1 unit.

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

•  $g\left(x\right)=-x^2-1$  

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

•  $g\left(x\right)=3x^2+1$  

Transform  $f\left(x\right)=\sqrt{x}$  by reflecting across the y-axis, translate left 1 unit, and translate down 1 unit.

•  $g\left(x\right)=-\sqrt{x-1}-1$  

•  $g\left(x\right)=\sqrt{-\left(x+1\right)}+1$  

•  $g\left(x\right)=\sqrt{-\left(x-1\right)}+1$  

•  $g\left(x\right)=\sqrt{-\left(x+1\right)}-1$  

Transform  $f\left(x\right)=x^2$  by translating left 3 units and down 1 unit.

•  $g\left(x\right)=\left(x+1\right)^2-3$  

•  $g\left(x\right)=\left(x+1\right)^2+3$  

•  $g\left(x\right)=\left(x-1\right)^2+3$  

•  $g\left(x\right)=\left(x+3\right)^2-1$  

Transform  $f\left(x\right)=x^2$  by a horizontal compression by a factor of 2 and reflecting across the x-axis.

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

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

•  $g\left(x\right)=-2x^2$  

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

Transform  $f\left(x\right)=\left|x\right|\$  by reflecting across the x-axis

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

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

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

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

Transform  $f\left(x\right)=\left|x\right|$  by horizontal compression by factor of 3.

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

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

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

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

What transformation is necessary to transform  $f\left(x\right)=x^2$  into that of  $g\left(x\right)=-x^2-2$  ?

• Reflect across the x-axis. Translate left 2 units.

• Reflect across the y-axis. Translate up 2 units.

• Reflect across the x-axis. Translate down 2 units.

• Reflect across the x-axis. Translate right 2 units.

 What transformation is necessary to transform  $f\left(x\right)=x^2$  into that of   $g\left(x\right)=\left(3x\right)^2-1$    ?

• Stretch horizontally by a factor of 3 and translate right 1 unit.

• Compress horizontally by a factor of 3 and translate right 1 unit.

• Stretch horizontally by a factor of 3 and translate left 1 unit.

• Compress horizontally by a factor of 3 and translate down 1 unit.

Write g(x) (dashed line) in terms of f(x) (solid line).

• $g\left(x\right)=-f\left(2x\right)$

• $g\left(x\right)=-2f\left(x\right)$

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

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

Write g(x) (dashed line) in terms of f(x) (solid line).

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

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

• $g\left(x\right)=f\left(3x\right)-1$

• $g\left(x\right)=-f\left(3x\right)$