Function Transformation Review

translation 2 units up

translation 2 units left

Vertical Stretch

translation 2 units right

Up 2 units

vertical compression, scale factor $$\frac{1}{2}$$

vertical stretch, scale factor 2

Right 2 Units

vertical stretch by factor of 2

up 3

right 3

left 3

reflected over the x axis

wider

narrower

same

impossible to tell

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

$$g\left(x\right)=2f\left(x+4\right)-3$$

$$g\left(x\right)=2f\left(x-4\right)+3$$

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

$$y=2x^2$$

$$y=-2x^2$$

$$y=-x^2$$

$$y=\left(x-1\right)^2$$

$$y=-\left|x\right|-7$$

$$y=\left|-x\right|-7$$

$$y=-\left|x-7\right|$$

$$y=-\left|x\right|+7$$

$$y=\left|-x\right|+7$$