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By: Nicholas Gerbracht, Gaby Soto, Erica Soto, Ana Marie Llamosas Page 396 problem #26 Process of analyzing a rational function Find horizontal and Oblique Asymptotes Find the intercepts Put rational function in factored form Simplify rational fucntion into lowest terms to find the Vertical Asymptote Determine the domain Plot the information on a graph Putting the function into rational form The function is already in rational form Determining the domain The domain is found by finding what makes the denominator = 0 Domain is all reals except -1 or 1 Also domain includes what the vertical asymptotes are. Simplifying into lowest terms Once you factor the denominator It is in lowest terms Finding horizontal and Vertical asymptotes Horizontal asymptote is N/A because the degree of the numerator is 1, and the degree of the denominator is 2. Since N<M therefor the H.A is Y= 0 Vertical asymptote are x=-1 x=1 Because those numbers make the denominator equal to 0. So the graph will get close to but never touch the x=-1 and 1 Finding the intercepts Finding the zeros (x-intercepts) ◦ By replacing y with zero you can find the x intercepts, i.e. the zeros x =0 ◦ x-intercept is (0,0) Finding the y-Intercepts ◦ Replace x with zero to find the y intercepts ◦ y-intercept is at (0,0) StepStep 3: Connect 1: Plot the the points dots, remember on a graphthe asymptotes Step 2: Plot asymptotes Plotting the information on a graph X F(x) -2 -2/3 -3 -3/8 -4 -4/15 -1/2 2/3 0 0 1/2 -2/3 2 2/3 3 3/8 4 4/15 Slide show made by Gaby Soto -determined horizontal/vertical asymptotesNick Gerbracht -made the powerpointErica Soto -X and Y intercepts and domainAna Marie Llamosas -Points on the graph-