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3.6 Rational Functions

3.6 Rational Functions. Sketching graphs of rational functions. Factor numerator and denominator Find intercepts. (x-int: zeros of numerator; y-int: where x=0) Find vertical asymptote (zeros of denom) Find horizontal asymptote (if any). n = degree of num m = degree of denom.

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3.6 Rational Functions

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  1. 3.6 Rational Functions

  2. Sketching graphs of rational functions • Factor numerator and denominator • Find intercepts. (x-int: zeros of numerator; y-int: where x=0) • Find vertical asymptote (zeros of denom) • Find horizontal asymptote (if any)

  3. n = degree of num m = degree of denom (still under step #4) • A) If n < m, then P(x) has a horiz asymp, y=0 • B) If n=m, then P(x) has horiz asymp, • C) If n > m, then P(x) has no horiz asymp.*

  4. (If n  m) • *If degree of num is one more than degree of denom, P(x) has a slant (oblique) asymp  use long division, then let x in remainder (remainder goes to 0) 5. Sketch graph. Use info from steps 1-4 and plot extra pts to fill in curves

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