Cube Root Graphs

Lesson :Cube Root Graphs

Today we will learn new family of functions

Meet the Cube Roots

• Domain: All Real Numbers

• Range: All Real Numbers

• Looks Like a "s"

• ***The a,h,k are back and surprise.... They do the same things they did to other functions

Negative Cube Roots

• Since -f(x) reflects the graph of f(x) in the x-axis, we get a backwards "s" (green graph)

• The two graphs together look like a chromosome

Poll

Does the function shown have a + or - in front of the equation?

• +

• -

Multiple Choice

How to you think the graph compares to the parent function?

• Right 5, Down 2

• Left 5, Down 2

• Right 2, Up 5

• Left 2, Up 5

Graphing Step 1: The "center" of the S

• Given by (h,k)

• This is because when you fill in h, the number under the cube root become 0

Example Step 1:

Graphing Step 2: Is the graph a normal "S" or a backwards "S"

• +a give "S"

• -a give backwards "s"

Step 3: Find the point one to the left/right

• use the "a" to figure out the "slope" of the "S"

• Plug in an x-value one bigger and one smaller than the h of the center

  
  

• OR from the center count up/down the "a" and then in the direction that will make your "S" the correct way

Example Step 3:

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Step 4: Get one more point on BOTH sides

• Plug in x-value 8 bigger/smalled than the h of the center (this guaranteed you get the cube rt of +/-8 which is neatly) 2

• OR count over 8 left/right from the center and go up/down 2a

Example Step 4:

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Draw the final graph

• Connect the dots

Example Step 4:

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