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Unit 7 –Rational Functions

Unit 7 –Rational Functions. Graphing Rational Functions. What to do first. FACTOR!!!! Factor either numerator, denominator, or both, before graphing. Do NOT simplify/cancel anything… yet. Graphing Rational Functions. To sketch these graphs, you must first identify…. The Mathtasitc 4!.

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Unit 7 –Rational Functions

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  1. Unit 7 –Rational Functions Graphing Rational Functions

  2. What to do first • FACTOR!!!! • Factor either numerator, denominator, or both, before graphing. • Do NOT simplify/cancel anything… yet.

  3. Graphing Rational Functions • To sketch these graphs, you must first identify… The Mathtasitc 4!

  4. M4: Vertical Asymptotes • Values of x that make the denominator 0. • Ex: After factoring we have: Denominator is 0 at x = 4 & x = -1. Those would be vertical asymptotes (graph cannot cross those lines).

  5. M4: Zeros • Values of x that make the numerator 0. • Ex: After factoring we have: Numerator is 0 at x = -3 & x = 2. Those points would be zeros (graph hits x-axis at those points).

  6. M4: Holes • Values of x that make both numerator & denominator 0. • Ex: After factoring we have: Numerator and denominator are 0 at x = -2. That point is a hole in the graph (graph passes through that point, but the function is undefined at that point).

  7. M4: Holes • Holes are NOT zeros. • They are not necessarily on the x-axis. • To find the coordinates of a hole, cancel the common binomial, and plug the value of x into what’s left to find the y value. After simplifying we have: Plugging -2 for x gives: A hole would be located at the point (-2, -4).

  8. M4: Horizontal Asymptote • Determined by degrees of numerator and denominator. • If numerator degree > denominator degree, no horizontal asymptote. • Ex. Numerator degree = 2, denominator degree = 1. No horizontal asymptote.

  9. M4: Horizontal Asymptote • Determined by degrees of numerator and denominator. • If numerator degree < denominator degree, there is a horizontal asymptote at y = 0. • Ex. Numerator degree = 1, denominator degree = 2. Horizontal asymptote at y = 0.

  10. M4: Horizontal Asymptote • Determined by degrees of numerator and denominator. • If numerator degree = denominator degree, the horizontal asymptote is at y = ratio of leading coefficients. • Ex. Degrees are both 2. Ratio of leading coefficients = 3/1. Horizontal asymptote at y = 3.

  11. Identifying the Mathtastic 4 • After finding asymptotes, zeros, and holes, graphs of rational functions are easy to sketch. • Be sure to use your graphing calculator to check your work.

  12. Identifying the Mathtastic 4 • Practice identifying the Mathtastic 4 with the functions presented in this presentation. • Keep in mind that all 4 will not always show up in a single function.

  13. Homework Textbook Section 8-4 (pg. 598): 33-42 Should be completed before Unit 7 Exam

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