transformations of cubic functions

​In this lesson you will be graphing cubic functions and determining transformations.

​Below are examples of cubic equations

Complete the table and graph the points for the parent cubic function.

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​Notes Part 1

Compare this graph and table to your graph and table from the parent function.

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The special point at (0,0) is now called the center point of the graph.

Cubic parent

function

Hotspot

Select the box represented by the center point of the cubic function

Graph using your calculator or create a table for each equation. Describe the transformations that occured compared to the parent function.

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Notes part 2

Now write the general transformations that occur.

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Notes part 3

Multiple Choice

Describe the transformations of the graph y = (x - 3)³ -2

• Right 3, Down 2

• Left 3, Up 2

• Right 3, Up 2

• Left 3, Down 2 

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 is the center point?

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

• (-4,3)

• (4,3)

• (-4,-3)

• (4,-3)

Multiple Choice

The graph shows the function f(x)=x³ in blue and another function g(x) in red.  Which could be the equation for g(x)?

• A.  g(x) = -x³

• B.  g(x) = x³ - 1

• C.  g(x) = (x + 1)³

• D.  g(x) = (x - 1)³

Multiple Choice

Describe the transformation of the graph  
y = ½x³

• Vertical compression by 1/2

• Horizontal compression by 1/2

• Vertical stretch by 2

• Horizontal stretch by 2

Multiple Choice

Describe the transformation of the graph  
y = (x - 1)³ + 7

• Up 7 and Right 1

• Reflect x-axis, Right 1, Up 7

• Reflect x-axis, Right 1, down 7

• Right 1 and down 7

Match

Match the following

• $$y=-2x^3$$

• $$y=\left(x-1\right)^3$$

• $$y=\left(x+1\right)^3$$

• $$y=-\frac{1}{2}x^3$$

• $$y=\left(x+1\right)^3-5$$

reflect over x, vertical stretch by 2

shift right 1

shift left 1

reflect over x, vertical compression by 1/2

shift left 1 down 5

• reflect over x, vertical stretch by 2

• shift right 1

• shift left 1

• reflect over x, vertical compression by 1/2

• shift left 1 down 5