POWER FUNTIONS AND MODELS
Lesson 3.2 is all about the properties of power functions of even and odd degrees. The most important concept for 3.2 is this: You should be able to sketch the graph of a power function, by looking at its degree and determining the end behavior of the graph.
The properties of power functions are discussed on pages 196 and 197. Here is an example: y = x^4 flattens at the vertex and gets more vertical as -1 < x < 1.
Read about these properties, and play with graphs on your TI-84 to learn more.
TI-84 exercises:
Graph y = x^2, y = x^2 + 1, and y = (x - 4)^2 + 1. What do you notice about the "end behavior" of all graphs. Now graph y = (x-1)(x-4). How is this graph different from the first three?
Leave me a comment with your observations and your questions on 3.2 :)
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3 comments:
I think that I have a good grasp of this lesson also. The only thing that might be troubling is remembering the properties of odd and even power functions.
These properties are on pages 196 and 197. The best way to learn them is to take a graph. calc. and study the odd funct. properties while looking at the graphs of several odd power function. You will notice that for every odd power function, the graph has origin symmetry. Check out y = x^3 and y + x^5. Now check out the domain and range for both of these functions. Notice that rule no. 3 applies to both functions. Finally, notice what happens to both graphs when x > 1 and x < -1. Look at y = x^7. Notice that all 4 rules still apply. Now, use the graphs of y = x^2, y = x^4 and y = x^6 to explore the properties of even power functions.
Being able to "see" the rules as you apply them to graphs makes learning them easier.
This lesson was pretty easy. I remember some of this stuff from Algebra II which is always helpful if you've seen it once before.
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