6.8 - Graph Radical Functions

6.8 - Graph Radical Functions

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Objectives:

• To graph radical funtions

• To transform radical functions

Inverse functions

You may recall that you can write an inverse of a function by exchanging the x and y in the equation.

The resulting graph will be reflected about the line y=x.

Radical functions

Open Ended

Following (0, 0), (1, 1), and (4, 2), what is the next data point in the function we just saw graphed?

Multiple Choice

Graph the function $$f\left(x\right)\ =\ \sqrt{x+1}$$  

Open Ended

What did you notice about the graph of $$f\left(x\right)=\sqrt{x+1}$$ ? What did you wonder? 

You probably recognize that square root functions follow pretty much the same transformation rules as the other functions we've studied, especially regarding the h, k, and a values.

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Multiple Choice

Describe the transformation of the graph of $$f\left(x\right)=\sqrt{x}-2$$  compared to the parent function  $$f\left(x\right)=\sqrt{x}$$  

• Translated 2 units left

• Translated 2 units right

• Translated 2 units down

• Translated 2 units up

Multiple Choice

Write the equation of a square root function that has been translated left 3 units, stretched vertically by a factor of 2, and reflected across the x-axis.

• $$f\left(x\right)=-2\sqrt{x-3}$$

• $$f\left(x\right)=-2\sqrt{x}+3$$

• $$f\left(x\right)=-3\sqrt{x-2}$$

• $$f\left(x\right)=-2\sqrt{x+3}$$

Poll

Select the image that most closely reflects how you feel you can graph radical functions and identify transformations of radical functions:

Great work!

Continue to work on the items on the notes page.