square root transformations and inverse practice Unit 6 D1-2

Shifted right 5, shifted down 2, and reflected over the x-axis

Reflected over the x-axis, vertical stretch by 2, and shifted right 5

Reflected over the x-axis, vertical stretch by 2, and shifted left 5

Shifted right 5, shifted down 2

(- ∞, -2 ]

[ -2, ∞ )

All Real Numbers

[ 0, ∞)

$$f\left(x\right)=\left(x-9\right)^2-2$$  DR x≥ 9

$$f\left(x\right)=\left(x+9\right)^2+2$$  DR x≥ -2

$$f\left(x\right)=\sqrt{x+9}+2$$  DR x≤9

$$f\left(x\right)=\sqrt{x-9}-2$$  DR x≥ -2

$$y=\frac{1}{5}x^2$$  ; DR [0,∞)

$$y=5x^2$$  DR [0,∞)

$$y=10x^2$$  DR [0,∞)

$$y=\sqrt{3x+1}$$  

DR [0,∞)

$$y=x^2-11$$  

$$y=x^2+11$$  

$$y=\left(x+11\right)^2$$  

$$y=\left(x-11\right)^2$$  

$$f\left(x\right)=\left(x-9\right)^2-2$$  DR x≤9

$$f\left(x\right)=\left(x-9\right)^2-2$$   DR x≥9

$$f\left(x\right)=\left(x-11\right)^2$$  

  DR x≥9

$$f\left(x\right)=\sqrt{x-9}-2$$  DR x≤9