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Copyright ©2015 Pearson Education, Inc. All right reserved. Section 3.6 Rational Functions Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved. Example: Graph Solution: Find the vertical asymptotes by setting the denominator equal to 0 and solving for x: Factor. Set each term equal to 0. Solve for x. Since neither of these numbers makes the numerator 0, the lines are vertical asymptotes of the graph. Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved. Example: Graph Solution: The horizontal asymptote can be determined by dividing both the numerator and denominator of by (the highest power of x that appears in either one). When is very large, the fraction is very close to 0, so the denominator is very close to 1 and is very close to 2. Hence, the line is the horizontal asymptote of the graph. Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved. Example: Graph Solution: Using this information and plotting several points in each of the three regions defined by the vertical asymptotes, we obtain the desired graph. Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.

y = 0 is the horizontal asymptote Degree of numerator < degree of denominator y = 0 is the horizontal asymptote

Degree of numerator = degree of denominator , y = 5x6 /2x6 = 5/2

Copyright ©2015 Pearson Education, Inc. All right reserved.

Copyright ©2015 Pearson Education, Inc. All right reserved.