Finding the Vertical and Horizontal Asymptotes of a Functions

The video tutorial explains how to determine the vertical and horizontal asymptotes and the domain of a rational function. It emphasizes that the domain excludes values that make the denominator zero. The vertical asymptote is identified by setting the denominator to zero. Horizontal asymptotes are determined by comparing the degrees of the polynomials in the numerator and denominator, with specific rules for when the degrees are equal, less, or greater. The video also mentions that slant asymptotes will be covered in another video.

What is the domain of a rational function?

• All real numbers

• All values of x that make the denominator zero

• All values of x except those that make the denominator zero

• All values of x that make the numerator zero

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

• Set the denominator equal to zero

• Set the numerator equal to zero

• Find the highest degree term

• Set both numerator and denominator equal to zero

What does a vertical asymptote represent on a graph?

• A line where the graph intersects

• A point where the graph crosses the x-axis

• A point where the graph crosses the y-axis

• A line where the graph approaches but never touches

When does a horizontal asymptote exist at y = 0?

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

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

• When the degrees of the numerator and denominator are equal

• When the degree of the numerator is zero

What happens when the degree of the numerator is greater than the degree of the denominator?

• There is a horizontal asymptote at y = 0

• There is no horizontal asymptote

• The graph has a vertical asymptote

• The horizontal asymptote is the ratio of leading coefficients