CA_GPS_39 - * Step 5: Find the intervals on which R is...

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Rev. S08 http://faculty.valenciacc.edu/ashaw/ COLLEGE ALGEBRA NAME: ________________________________ GPS # 39 4.5 RATIONAL FUNCTIONS AND RATIONAL EQUATIONS III Class Time: ____________ Date: __________ Useful Guidelines: To analyze the graph of a rational function, ) ( ) ( ) ( x q x p x R = , in lowest terms: * Step 1: Find the domain of the rational function. * Step 2: Find the x -intercept(s), if any (let 0 ) ( = x p when ) ( x R is in lowest term), and the y -intercept(s), ) 0 ( R . * Step 3: Write R in lowest term and find the real zeros of the denominator (vertical asymptotes). * Step 4: Find the horizontal or slant asymptotes, if any.
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Unformatted text preview: * Step 5: 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 . 1. Analyze the graph of the following rational function by following Step 1 through 6 above. 4 24 ) ( 2 ! = x x R 2. Solve the rational equation and give the solution set. a) 3 1 5 ! = + ! x x b) 2 4 16 2 = ! x...
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