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