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2.6 Graphing Rational Functions p(x) and q(x) are polynomials and ≠ 0

2.6 Graphing Rational Functions p(x) and q(x) are polynomials and ≠ 0. To find the y-intercept of the graph, find f(0). The domain is related to the vertical asymptotes ! Find the values of q(x) that make the function undefined!.

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2.6 Graphing Rational Functions p(x) and q(x) are polynomials and ≠ 0

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  1. 2.6 Graphing Rational Functionsp(x) and q(x) are polynomials and ≠ 0 To find the y-intercept of the graph, find f(0). The domain is related to the vertical asymptotes! Find the values of q(x) that make the function undefined! To find the x-intercepts or zeros of the graph, find the values that make p(x) = 0.

  2. Identify x and y intercepts: a) b) c) d)

  3. Investigating Horizontal Asymptotes Test the value x = 2 with the three functions below. What do you notice about the results? Describe a relationship you may see. How might the results link to the degree of the numerator and denominator?

  4. Horizontal Asymptotes: 3 cases a.) If m = n or the degree is the same, then the horizontal asymptote is found by the ratio of the leading coefficients of the polynomials p(x) and q(x). b.) If n > m or the degree of the numerator is larger than the degree of the denominator, then there is no horizontal asymptote! c.) If n < m or the degree of the denominator is larger than the degree of the numerator, then the horizontal asymptote is y = 0.

  5. Identify vertical & horizontal asymptotes: a) b) c) d)

  6. Identify Domain and Range: a) b) c) d)

  7. Oblique/Slant Asymptotes A slant asymptote (or oblique asymptote) exists for a rational function if the degree of the numerator is exactly one more than the degree of the denominator! To find the linear equation of the slant asymptote, you must divide the polynomials and find the quotient.( Disregard the remainder)

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