Objective: Students will be able to graph rational functions using their asymptotes and zeros.
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Transcript of Objective: Students will be able to graph rational functions using their asymptotes and zeros.
5.4 – Graphing Rational Functions
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 HyperbolasIdentify the asymptotes, domain, and range of the
following rational functions. Example 1:
Asymptotes:
Domain:
Range:
Example 2:Asymptotes:
Domain:
Range:
Rational Function PropertiesDiscontinuous 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 AsymptotesDirections: Identify the zeros and vertical asymptotes of the
function. Then graph. Example 3:
Zeros:Vertical Asymptote:
Example 4
Zeros:Vertical Asymptote:
Example 5Directions: Identify the zeros and asymptotes of each
function. Then graph using the graphing calculator.
f(x) =
Example 6f(x) =
Example 7f(x) =
Homework for tonight Homework # _____
Textbook pg. 345 # 20, 21, 23, 25, 26, 27