11.2 – Graphing Rational Functions

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Presentation transcript:

11.2 – Graphing Rational Functions Definitions of the Day (DODs) Rational Function Asymptote

Examples: Definition: Rational Function: A function that can be written in the form Examples:

Definition: A line is an asymptote of a graph if the graph of the function gets closer and closer to the line, but does not cross it. Example: The red lines are asymptotes. One line is a vertical asymptote (x = 0). The other line is a horizontal asymptote (y = 0). Notice that the graph approaches the asymptotes, but does not cross them.

Evaluate each rational function for x = 3. Finding Vertical Asymptotes Evaluate each rational function for x = 3.

To find vertical asymptotes, we will set the denominator equal to zero and solve for x. Find the vertical asymptote for each rational function.

Steps to graphing a rational function: 1. Find the vertical asymptote. The vertical asymptote is where the denominator equals zero. 2. Make a table of values around the asymptote. 3. Draw the graph (remember to show the asymptote by using a dashed line).

Graphing a rational function Graph the function

Graphing a rational function Graph the function

Your Turn!! Evaluate the rational function for x = -2 Graph the following function

Sentence Frames A rational function is a __________ over another ___________. To find a vertical asymptote, I need to _________________________________________.