Learn how to graph a rational function when the function intercepts horizontal asymptote

The video tutorial explains how to graph rational functions by identifying vertical and horizontal asymptotes. It begins with finding vertical asymptotes by setting the denominator to zero and solving for x. The tutorial then covers horizontal asymptotes by comparing the degrees of the numerator and denominator. Finally, it demonstrates graphing the function using a graphing calculator and evaluating points around the asymptotes.

What is the first step in identifying vertical asymptotes of a rational function?

• Find the derivative of the function

• Set the denominator equal to zero

• Graph the function

• Set the numerator equal to zero

How can you determine if a vertical asymptote is actually a hole in the graph?

• By checking if the numerator is zero

• By checking if the factors can be canceled out

• By finding the horizontal asymptote

• By using a graphing calculator

What condition must be met for the horizontal asymptote to be y = 0?

• The degree of the numerator is less than the degree of the denominator

• The degree of the numerator is greater than the degree of the denominator

• The numerator is a constant

• The degree of the numerator is equal to the degree of the denominator

Which tool is recommended for plotting the graph of a rational function?

• A ruler

• A graphing calculator

• A protractor

• A compass

What is the significance of choosing values close to the asymptotes when graphing?

• To better understand the behavior of the graph near asymptotes

• To find the exact points of intersection

• To avoid errors in calculations

• To simplify the graphing process

What happens to the graph of a rational function at a vertical asymptote?

• It approaches but never crosses the asymptote

• It crosses the asymptote

• It forms a parabola

• It becomes a straight line

Is it possible for a graph to cross a horizontal asymptote?

• Only if the denominator is zero

• Yes, it can cross at certain points

• No, it never crosses

• Only if the numerator is zero