Cubic Root Functions

Up 5 and Left 4 

Reflect x-axis, Left 4, Up 5

Reflect x-axis, Right 4, Up 5

Right 4 and up 5

Horz shift right 2      Vert shift up 4

Horz shift left 2    Vert shift up 4

Horz shift right 2      Vert shift down 4

Horz shift left 2      Vert shift up 4

Pearl

Patrick

Squidward

Sandy

$$y=-\left(x-1\right)^3+4$$

$$y=\left(x-1\right)^3+4$$

$$y=-\left(x+1\right)^3+4$$

$$y=\left(x+1\right)^3+4$$

linear

quadratic

cube root

cubic

f(x) = (x + 2)³

f(x) = (x - 2)³

f(x) = ∛(x + 2)

f(x) = ∛(x - 2)

Shrink by 2, Reflected over y-axis, Right 5

Stretch by 2, Reflected over x-axis, Left 5

Stretch by 2, Reflected over x-axis, Right 5

Shrink by 2, reflected over y-axis, Left 5

Right 6

Left 6

Up 6

Down 6

$$y=\sqrt[3]{x-3}+5$$

$$y=\sqrt[3]{x-3}-5$$

$$y=\sqrt[3]{x+3}+5$$

$$y=\sqrt[3]{x+3}-5$$

1/4 ∛(x + 9)

1/4 ∛(x - 9)

- 1/4 ∛(x + 9)

- 1/4 ∛(x - 9)

$$f\left(x\right)=-\sqrt[3]{x+3}-1$$  

$$f\left(x\right)=-\sqrt[3]{x-3}-1$$  

$$f\left(x\right)=\sqrt[3]{x+3}-1$$  

$$f\left(x\right)=\sqrt[3]{x-1}+3$$  

Cube Root Function

Cubic Function

Polynomial Function

Square Root Function

Vertical stretch by 2 and down 4

Horizontal compression by ½ and down 4

Vertical stretch by 2 and up 4

Horizontal compression by ½ and right 4

$$f\left(x\right)=\sqrt[3]{x+2}-5$$

$$f\left(x\right)=\sqrt[3]{x-5}+2$$

$$f\left(x\right)\ =\ \sqrt[3]{x+5}+2$$