Asymptotes and Holes in Graphs

The video tutorial covers graphing rational functions, focusing on finding x-intercepts, vertical and horizontal asymptotes, slant asymptotes, and holes. It provides step-by-step examples to illustrate these concepts, including factoring and graphing techniques. The tutorial concludes with encouragement for the upcoming quiz.

What is the first step in finding the x-intercepts of a rational function?

• Find the degree of the denominator

• Find the degree of the numerator

• Set the denominator equal to zero

• Set the numerator equal to zero

What is the result of setting the numerator of a rational function to zero?

• Finding the slant asymptote

• Finding the zeros

• Finding the horizontal asymptote

• Finding the vertical asymptote

How do you determine the vertical asymptotes of a rational function?

• Perform long division

• Compare the degrees of the numerator and denominator

• Set the denominator equal to zero

• Set the numerator equal to zero

What is the result of setting the denominator of a rational function to zero?

• Finding the zeros

• Finding the vertical asymptotes

• Finding the horizontal asymptotes

• Finding the slant asymptotes

If the degree of the numerator is less than the degree of the denominator, what is the horizontal asymptote?

• y = 0

• There is no horizontal asymptote

• y = 1

• y = the leading coefficient of the numerator

What is the significance of the leading coefficients in determining the horizontal asymptote?

• They determine the vertical asymptote

• They have no significance

• They determine the slant asymptote

• They determine the horizontal asymptote

What happens if the degrees of the numerator and denominator are equal?

• There is no horizontal asymptote

• The horizontal asymptote is y = 0

• There is a slant asymptote

• The horizontal asymptote is determined by the leading coefficients

What happens if the degree of the numerator is one more than the degree of the denominator?

• There is a horizontal asymptote

• There is a slant asymptote

• There is a vertical asymptote

• There is no asymptote

How do you find the slant asymptote of a rational function?

• By setting the numerator to zero

• By comparing the leading coefficients

• By setting the denominator to zero

• By performing long division

How do holes in the graph of a rational function occur?

• When the denominator is zero

• When the numerator is zero

• From cancellations of common factors

• When the degrees of numerator and denominator are equal