Radical and Inverse Variation Functions

Shifted down 2

Shifted up 2

Shifted left 2

Shifted right 2

$$y=\sqrt{x-5}-1$$

$$y=\sqrt{x+5}-1$$

$$y=\sqrt{x-5}+1$$

$$y=\sqrt{x+5}+1$$

$$\left(-\inf,\ -2\right]$$  

$$\left[-2,\ \inf\right)$$  

$$\left[0,\ \inf\right)$$  

$$\left(-\inf,\ 0\right)$$  

[4, inf)

[-2, inf)

(-inf, 2]

[2, inf)

Vertical Stretch by a factor of 2; translated down 5 units 

Shifted right 2 units and down 5 units 

Vertical stretch by a factor of 2; translated left 5 units

Vertical stretch by a factor of 2; translated right one unit 

Reflect over a horizontal line, left 1, up 2

Reflect over a vertical line, left 1, down 2

Reflect over a vertical line, right 1, up 2

Reflect over a horizontal line, right 1, down 2

$$y=-\sqrt{x+1}$$

$$y=\sqrt{x+1}$$

$$y=-\sqrt{x}-1$$

$$y=\sqrt{x}+1$$

$$y=2\sqrt{x}-4$$

$$y=-\sqrt{x-4}$$

$$y=2\sqrt{x}$$

$$y=2\sqrt{x}+4$$

$$y=\sqrt{x}+2$$

$$y=\sqrt{x}-2$$

$$y=\sqrt{x+2}$$

$$y=\sqrt{x-2}$$

Domain: all real numbers

Range: all real numbers

Domain: all real numbers $$x\ne0$$

Range: all real numbers $$y\ne0$$