Reference Notes 6 - Reference 6 Finding Features in the...

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page 10 of 48 Reference 6: Finding Features in the Graph of a Rational Function Part 1: Analyze the standard form of the function. Determine the y -intercept by computing . The y -intercept is the point . Determine the right-end behavior by computing . Use the technique of identifying dominant terms. If , then the right end of the graph goes up. If , then the right end of the graph goes down. If , then the line will be a horizontal asymptote for the right end of the graph. Because is a rational function, in this case, we know that the line will also be a horizontal asymptote for the left end of the graph. If there is not a horizontal asymptote, then determine the left-end behavior by computing . Use the technique of identifying dominant terms. If , then the left end of the graph goes up. If , then the left end of the graph goes down. Part 2: Analyze the factored form of the function. Determine the effect that each factor will have on the graph of the function. If a factor of the form appears in the numerator only, then the graph will have an x-
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