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Warm Up

Warm Up . Solve each rational equation or inequality. Homework Answers. Rational Functions. Domain, Asymptotes and Holes. Objectives. You will be able to identify the domain the y-intercept the vertical asymptotes the end behavior asymptote

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Warm Up

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  1. Warm Up Solve each rational equation or inequality.

  2. Homework Answers

  3. Rational Functions Domain, Asymptotes and Holes

  4. Objectives You will be able to identify the domain the y-intercept the vertical asymptotes the end behavior asymptote and coordinates of any holes in the graph of a rational function.

  5. Let’s talk about the domain… • Remember: “You can’t divide by zero” • To find the domain of a rational function set the denominator equal to zero and solve for the real solutions. The domain is all real numbers except for those values.

  6. Find the domain of each of the following rational functions.

  7. What about the vertical asymptotes and holes? • Everywhere the function is undefined is either a VA or a hole in the graph… • look at the domain 

  8. Determine coordinates of holes in the graph and write the equation for the vertical asymptote(s)

  9. Determine coordinates of holes in the graph and write the equation for the vertical asymptote(s)

  10. Determine coordinates of holes in the graph and write the equation for the vertical asymptote(s)

  11. Determine coordinates of holes in the graph and write the equation for the vertical asymptote(s)

  12. What about the end behavior asymptotes? • To find the end behavior asymptote simply divide the denominator into the numerator…the end behavior asymptote is the quotient.

  13. But a “Hint” about those E.B.A.s • Bottom Heavy: degree of the bottom is bigger than the degree of the top • EBA is always y = 0 • Equal:degree of the bottom is the same as the degree of the top • EBA is always y = leading coefficient leading coefficient • Top Heavy: degree of the top is bigger than the degree of the bottom • no trick  you have to divide.

  14. Identify the EBA for each of the following.

  15. PRACTICEIdentify the domain, vertical asymptote(s), x- and y-coordinates of holes, and end behavior asymptotes.

  16. What are the equations of the asymptotes?Describe the equation of the graph.

  17. What are the equations of the asymptotes?Describe the equation of the graph.

  18. What are the equations of the asymptotes?Describe the equation of the graph.

  19. What are the equations of the asymptotes? What is the x-coordinate of the hole?Describe the equation of the graph.

  20. Match each graph to the correct equation…

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