Graphing Rational Functions and Asymptotes

The video tutorial covers graphing rational functions with a focus on asymptotes. It begins with an introduction to the topic, followed by a detailed process for graphing these functions. Three examples are provided: the first involves a function with one vertical asymptote, the second deals with functions where the numerator and denominator have equal degrees, and the third requires factoring. The tutorial emphasizes understanding excluded values, vertical and horizontal asymptotes, and using tables of values to sketch graphs accurately.

What is the first step in the process of graphing rational functions?

• Sketch the graph

• Determine the horizontal asymptote

• Completely factor both the numerator and denominator

• Find the x and y intercepts

How do you determine the excluded values of a rational function?

• Find the y-intercepts

• Set the numerator equal to zero

• Set the denominator equal to zero

• Find the x-intercepts

What indicates a vertical asymptote in a rational function?

• When the factor cancels out

• When the factor does not cancel out

• When the numerator is zero

• When the denominator is one

In Example 1, what is the vertical asymptote of the function?

• y = 0

• x = -5

• y = -5

• x = 5

In Example 1, what is the horizontal asymptote of the function?

• y = 5

• y = -5

• x = 0

• y = 0

In Example 2, what is the vertical asymptote of the function?

• x = 3

• x = -3

• y = 1

• y = -1

In Example 2, what is the horizontal asymptote of the function?

• y = -3

• y = 3

• x = 1

• y = 1

In Example 3, what are the vertical asymptotes of the function?

• x = 5 and x = -3

• y = 3 and y = -5

• x = 3 and x = -5

• y = 5 and y = -3

In Example 3, what is the horizontal asymptote of the function?

• x = 0

• y = 5

• y = 0

• y = -5

What should you do if you need more points to sketch the graph accurately?

• Use only the intercepts

• Guess the points

• Ignore the additional points

• Use a table of values to plot more points