This document contains notes from a math class on radical and rational functions. It discusses drawing graphs of radical functions, including simple radical graphs using intercepts and shape. It notes rules for graphing root functions, such as invariant points where y=0 and y=1, and whether the root graph is above or below the original function depending on whether y is between 0 and 1 or greater than 1. Examples are given of graphing the square root and cube root of quadratic and cubic functions. Students are assigned homework problems related to these concepts.

1. 2.1 Notes.notebook March 12, 2013
Unit 2: Radical and Rational Functions
In the last unit we looked at polynomial
functions and how to draw their graphs.
In this unit we will look at 2 other types of
functions and their graphs.
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2. 2.1 Notes.notebook March 12, 2013
2.1 Radical Functions
Interesting!
Notice!
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3. 2.1 Notes.notebook March 12, 2013
Notice this is the same as the Notice this graph is NOT shifted
graph of shifted 4 units to 2 units to the left. What
the left. happened?
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4. 2.1 Notes.notebook March 12, 2013
Simple radical graphs can be drawn using intercepts and
the general shape of
Draw a quick sketch of the following:
1) 2)
3)
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5. 2.1 Notes.notebook March 12, 2013
When equations get complicated there are some visual clues we can notice to
arrive at conclusions about radical graphs. Look at the diagrams again
of the 2 linear examples from before.
If y=f(x) is the linear function then:
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6. 2.1 Notes.notebook March 12, 2013
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7. 2.1 Notes.notebook March 12, 2013
The same rules apply to the root graphs of higher order functions.
• The invariant points occur where y=0 and y=1
• The root graph is above the original function where y is between 0 and 1
• The root graph is below the original function where y>1
• The root graph does not exist where the original function has y<0
Invariant Point
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8. 2.1 Notes.notebook March 12, 2013
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9. 2.1 Notes.notebook March 12, 2013
Again, the same rules apply to this cubic function
Graph y=x3­4x on your calculator
Graph its root graph.
Notice it follows the patterns we
have said.
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10. 2.1 Notes.notebook March 12, 2013
Compare it to your algebraic answer of this question.
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11. 2.1 Notes.notebook March 12, 2013
Homework: Page 89 #1,2,5,6,8a,
9,10,11,12
Multiple Choice 1,2
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