Square Root Functions

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

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

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

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

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

reflects over horizontal line, vertical stretch by 3, right 2, up 1

reflects over vertical line, vertical compression by -3, left 2, up 1

reflects over horizontal line, vertical stretch by -3, left 2, up 1

reflects over vertical line, vertical compression by 1/3, right 2, up 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

{x ∣ x ≥ 1}

{x ∣ x ≤ 1}

{x ∣ x ≥ -3}

{x ∣ x ≥ -1}

{f(x) ∣ f(x) ≥ -2}

{f(x) ∣ f(x) ≥ 2}

{f(x) ∣ f(x) ≥ 4}

{f(x) ∣ f(x) ≥ -4}

(0,0)

(9,0)

(0,-3)

(1,1)

(-1,0)

(0,-1)

(0,3)

(3,0)

(-4,0)

(4,0)

(-18,0)

(18,0)