Function Transformations

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

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

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

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

right 3, down 2

up 3, left 2

left 3, up 2

left 3, down 2

Vertical compression (wider)

Vertical stretch (narrower)

Vertical compression (wider) and reflection over x-axis

Vertical stretch (narrower) and reflection over x-axis

Horizontal shift left 6, vertical shift up 2

Horizontal shift left 6, vertical shift down 2

Horizontal shift right 6, vertical shift down 2

Horizontal shift right 6, vertical shift up 2

$$f(x)=|x-4|+3$$  

$$f(x)=|x-3|+4$$  

$$f(x)=|x-4|-3$$  

$$f(x)=|x+4|+3$$  

$$y=-|x+2|-7$$  

$$y=|x-2|-7$$  

$$y=-|x-2|-7$$  

$$y=-|x-2|+7$$  

Left 4, up 9

Left 4, down 9

Right 4, up 9

Right 4, down 9