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| How to Find the Domain of a Rational Function |
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Definition
1.) Make Denominator Equal Zero
2.) Factor the Denominator (If Necessary)
3.) Solve to find what numbers are excluded from the domain
4.) Use unions to denote the numbers excluded from the domain |
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| Graph of a rational function... |
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Definition
| Cannot Cross a Vertical Asymptote |
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Term
| How Do You Find Vertical Asymptotes? |
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Definition
1.) Simplify the Rational Function By Eliminating Common Roots (When you eliminate a common root you also eliminate a number from your domain that is opposite the sign of the common root)
2.) Make Denominator of Rational Function Equal Zero
3.) Solve to find the vertical asymptotes |
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Term
| What is a Rational Function? |
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Definition
| r=p/q, if q does not equal zero, and p and q are polynomials |
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Term
| How to Find Horizontal Asymptotes? |
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Definition
1.) Divide the leading terms of the polynomials in the numerator and the denominator: anX^n/bmX^m
2.) If m=n y=an/bm
3.) If m
4.) If m>n y=0 |
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Term
| How Do You Graph A Rational Function? |
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Definition
1.) Your x-intercept are the zeroes of the numerator that are within your domain
2.) Your y-intercept is the rational function where all x's equal zero.
3.) Graph All Asymptotes [Remember You Can Cross Horizontal Asymptotes, just not Vertical Asymptotes]
4.) There is Some Funky Way to Tell How Asymptotes Behave In Relation to Elements of the Domain.
5.) Graph Asymptotes Accordingly |
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Term
| How Do You Find An Oblique Asymptote? |
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Definition
p(x)/q(x), where degree of p=degree of q-1
There is no horizontal asymptote
The Oblique Asymptote is at y=ax+b |
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