Objective: Students will be able to graph rational functions using their asymptotes and zeros.

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A rational function is a function whose rule can be written as a ratio of two polynomials. The parent rational function is f(x) = . Its graph is a.

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Presentation transcript:

Objective: Students will be able to graph rational functions using their asymptotes and zeros.

Graphs of Rational Functions An asymptote of a function is a line that continuously approaches the function but never touches it at any point.

Determining Properties of Hyperbolas Identify the asymptotes, domain, and range of the following rational functions. Example 1: Asymptotes: Domain: Range:

Example 2: Asymptotes: Domain: Range:

Rational Function Properties Discontinuous function – a function whose graph has one or more gaps or breaks. (ex: hyperbola) Continuous function – a function whose graph has no gaps or breaks. (ex: linear, quadratic, polynomial)

Graphing Rational Functions with Vertical Asymptotes Directions: Identify the zeros and vertical asymptotes of the function. Then graph. Example 3: Zeros: Vertical Asymptote:

Example 4 Zeros: Vertical Asymptote:

Example 5 Directions: Identify the zeros and asymptotes of each function. Then graph using the graphing calculator. f(x) =

Example 6 f(x) =

Example 7 f(x) =

Homework for tonight Homework # _____ Textbook pg. 345 # 20, 21, 23, 25, 26, 27