Identify Asymptotes and intercepts of Rational Function

The video tutorial covers the concept of asymptotes in rational functions, focusing on horizontal, vertical, and slant asymptotes. It explains how to determine the existence of these asymptotes based on the degrees of the numerator and denominator. The tutorial also discusses the possibility of holes in the graph and provides a detailed walkthrough of using long division to find slant asymptotes. The importance of the quotient in determining the slant asymptote is highlighted, and the video concludes with a brief overview of finding x and y intercepts.

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

• The graph has a hole.

• A horizontal asymptote exists.

• A slant asymptote may exist.

• A vertical asymptote exists.

What is the first step in finding a slant asymptote?

• Set the numerator equal to zero.

• Perform polynomial division.

• Find the y-intercept.

• Check for holes in the graph.

Why is it important to consider the remainder in polynomial division when finding slant asymptotes?

• The remainder determines the y-intercept.

• The remainder helps find the x-intercept.

• The remainder affects the existence of vertical asymptotes.

• The remainder is irrelevant for slant asymptotes.

How do you find the x-intercept of a function?

• Set the denominator equal to zero.

• Perform polynomial division.

• Set the numerator equal to zero.

• Find the slant asymptote.

What is the y-intercept of a function if the constant over constant is given as four?

• Y = 2

• Y = 4

• Y = 1

• Y = 0