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8-3 Rational Functions

8-3 Rational Functions. Unit Objectives: Graph a rational function Simplify rational expressions. Solve a rational functions Apply rational functions to real-world problems Today’s Objective: I can graph a rational function. Rational Function:. and are polynomials. Hole.

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8-3 Rational Functions

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  1. 8-3Rational Functions Unit Objectives: Graph a rational function Simplify rational expressions. Solve a rational functions Apply rational functions to real-world problems Today’s Objective: I can graph a rational function.

  2. Rational Function: and are polynomials • Hole • Asymptote Continuous Graph: No breaks in graph • Discontinuous Graph: • Breaks in graph

  3. Discontinuities: • Where the Denominator = zero Domain: • All real numbers (except discontinuities Vertical Asymptotes: Non-removable Holes: Removable Same factor in numerator and denominator Discontinuity: or or Domain: All reals but All reals but Holes: V. Asymp:

  4. Horizontal Asymptotes: • Leading term of numerator and denominator (standard form) No horizontal asymptote No horizontal asymptote Range: All real numbers except horizontal asymptote & holes

  5. Graph: Find and graph asymptotes & holes Find and graph additional points → each side of v. asymptote Sketch graph • Discontinuities: Hole: • None V. Asymp.: H. Asymp.: Domain: Range:

  6. Graph: • Discontinuities: Hole: V. Asymp.: Domain: Range: H. Asymp.:

  7. Graph: Discontinuities: Hole: V. Asymp.: H. Asymp.: Pg. 521 #13-31 odds Domain: Range:

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