Cubic and Cube Root Transformations

Cubic Functions

Take a pic of this chart to help You

Multiple Choice

Which of these represents a CUBIC function?

Multiple Choice

What is the y-intercept of the following cubic function?

• (1, 0)
• (0, 2)
• (-1, 0)
• (2, 0)

Multiple Choice

Which of the following is the graph of $$y=\left(x+5\right)^3-1$$  

Multiple Choice

Which of the following is the graph of $$y=\left(x-2\right)^3-4$$  

Multiple Choice

Describe the transformation of the graph  y = -(x - 4)³ + 5

• Up 5 and Left 4 

• Reflect x-axis, Left 4, Up 5

• Reflect x-axis, Right 4, Up 5

• Right 4 and up 5

Multiple Choice

What are the transformations?
y=(x-2)³+4

• 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

Multiple Choice

Who is Spongebobs Best friend? (BEST friend)

• Pearl

• Patrick

• Squidward

• Sandy

Multiple Choice

Which of the following is the graph of $$y=\left(x+5\right)^3-1$$  

Multiple Choice

Which of the following is the equation of the cubic function graphed above

• $$y=-\left(x-1\right)^3+4$$

• $$y=\left(x-1\right)^3+4$$

• $$y=-\left(x+1\right)^3+4$$

• $$y=\left(x+1\right)^3+4$$

Multiple Choice

Name the parent function.

• linear

• quadratic

• cube root

• cubic

Multiple Choice

What is the equation of this function?

• f(x) = (x + 2)³

• f(x) = (x - 2)³

• f(x) = ∛(x + 2)

• f(x) = ∛(x - 2)

Multiple Choice

Describe the transformation of the graph  y = -2(x + 5)³ 

• 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

Multiple Choice

Describe the transformation of the graph  y = (x)³  + 6

• Right 6

• Left 6

• Up 6

• Down 6

Cube Root Functions

Multiple Choice

What kind of function is represented by the graph?

• Cube Root Function
• Cubic Function
• Polynomial Function
• Square Root Function

Multiple Choice

Match the equation with the graph

• $$y=\sqrt[3]{x-3}+5$$

• $$y=\sqrt[3]{x-3}-5$$

• $$y=\sqrt[3]{x+3}+5$$

• $$y=\sqrt[3]{x+3}-5$$

Multiple Choice

If f(x) = ∛(x) is reflected over the x-axis, vertically compressed by a factor of 1/4, and shifted left 9, which equation is correct?

• 1/4 ∛(x + 9)

• 1/4 ∛(x - 9)

• - 1/4 ∛(x + 9)

• - 1/4 ∛(x - 9)

Multiple Choice

Which function matches the graph?

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

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

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

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

Multiple Choice

What kind of function is represented by the graph?

• Cube Root Function

• Cubic Function

• Polynomial Function

• Square Root Function

Multiple Choice

Identify the Transformations. 

• 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

Multiple Choice

Identify the function that corresponds with the graph.

• $$f\left(x\right)=\sqrt[3]{x+2}-5$$

• $$f\left(x\right)=\sqrt[3]{x-5}+2$$

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