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Unformatted text preview: COLLEGE ALGEBRA NAME: ________________________________ GPS # 38 Class Time: ____________ Date: __________ 4.5 RATIONAL FUNCTIONS AND RATIONAL EQUATIONS II Useful Guidelines: To analyze the graph of a rational function, R( x) = p( x) , in lowest terms: q( x) * Step 1: * Step 2: * Step 3: * Step 4: * Step 5: Find the domain of the rational function. Find the x-intercept(s), if any (let p ( x) = 0 when R( x) is in lowest term), and the y-intercept(s), R(0) . Write R in lowest term and find the real zeros of the denominator (vertical asymptotes). Find the horizontal or slant asymptotes, if any. Find the intervals on which R is above the x-axis and the intervals on which R is below the x-axis. [Hint: pick a point between the zeros obtained from both the numerator and the denominator.] * Step 6: Graph the asymptotes, if any, plot the points, connect the points and graph R. Analyze the graph of each function by following Step 1 through 6 above. 2 x ! 10 R( x) = 1) x 2) Rev. S08 R( x) = x 2 ! 25 x!5 ...
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This note was uploaded on 10/18/2011 for the course MAC 1105 taught by Professor Russel during the Summer '07 term at Valencia.

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