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3.6 Graph Rational Functions

3.6 Graph Rational Functions. 3.6, 3.8, 3.12 Quiz: May 12 3.1, 3.3, 3.6, 3.8, 3.12, 3.13 Test: May 18 Final Exam: May 25. Vocabulary. A rational function has a rule given by a fraction whose numerator and denominator are polynomials and whose denominator is NOT zero!

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3.6 Graph Rational Functions

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  1. 3.6Graph Rational Functions 3.6, 3.8, 3.12 Quiz: May 12 3.1, 3.3, 3.6, 3.8, 3.12, 3.13 Test: May 18 Final Exam: May 25

  2. Vocabulary • A rational function has a rule given by a fraction whose numerator and denominator are polynomials and • whose denominator is NOT zero! • An asymptote is a line that a graph approaches more and more closely but NEVER crosses or touches.

  3. Asymptotes The horizontal asymptote is y = k. Set the denominator equal to zero and solve for x. This gives you the vertical asymptote. (x = h)

  4. The Parent Rational Function Graph: y = 1/x

  5. Example 1: • Graph y = 3/x • Since we multiply 1/x times 3…we are stretching by 3. • Which means our graph is “above” the parent function.

  6. Example 2: • Graph y = 1/3x • Since we are multiplying 1/x by 1/3…we are shrinking the graph. • Which means our graph is “below” the parent function.

  7. Example 3: • Graph y = -2/x • Since we are multiplying 1/x by -2, the graph flips (b/c of the negative) and stretches. • Which means our graph is now on the other sides.

  8. Example 4: • Graph • Identify Domain and Range

  9. Example 5: • Graph • Identify Domain and Range

  10. Homework • P. 153 #9-14, 16-24

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