One last problem:
| Graph |
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2
things |
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y-intercepts: Find
f(0) |
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x-intercepts:
numerator =
0, solve |
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Vertical asymptotes:
denominator =
0, solve |
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Horizontal asymptote: |
| Look at |
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Hey -- it's a
slant! |
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Slant asymptote: |
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OK, Skippy -- are you ready to graph this bad boy?
Intercepts and asymptotes:
First, let's think about the left and right neighborhoods:
Here's what we've got -- see if you can figure it out!
Graphs hug asymptotes.
These guys are functions.
He can ONLY cross the x-axis at x = 0.
Can he do this?
So, it must be like this:
What about the middle neighborhood?
We'll need to quickie plot two points... Try it before going on.
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NOTE: A common mistake that students make is to think that a graph cannot cross a slant or horizontal asymptote. This is not the case! A graph CAN cross slant and horizontal asymptotes (sometimes more than once). It's those vertical asymptote critters that a graph cannot cross. This is because these are the bad spots in the domain.
YOUR TURN:
| Graph |
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