Rational Functions: Asymptotes and Holes

This video tutorial explains how to find points of discontinuity and vertical asymptotes in rational functions by identifying domain restrictions. It covers factoring the denominator to find domain restrictions, simplifying the fraction to identify holes, and calculating the coordinates of these holes. The video concludes with identifying vertical asymptotes and summarizing the key concepts.

What are the two main concepts discussed in the video related to rational functions?

• Vertical asymptotes and range restrictions

• Horizontal asymptotes and domain restrictions

• Points of discontinuity and vertical asymptotes

• Points of discontinuity and horizontal asymptotes

Why is it important to consider the denominator in a rational function?

• To calculate the y-intercepts

• To avoid division by zero

• To find the range of the function

• To determine the x-intercepts

How do you find the domain restrictions of a rational function?

• By setting the numerator equal to zero

• By finding the x-intercepts

• By finding the y-intercepts

• By setting the denominator equal to zero

What is the next step after finding the domain restrictions in a rational function?

• Finding the range

• Simplifying the function

• Graphing the function

• Calculating the intercepts

What happens when a factor in the numerator cancels with a factor in the denominator?

• It creates a hole in the graph

• It changes the range of the function

• It creates a horizontal asymptote

• It creates a vertical asymptote

How do you find the y-coordinate of a hole in the graph?

• By setting the denominator equal to zero

• By finding the x-intercepts

• By substituting the x-coordinate into the simplified function

• By setting the numerator equal to zero

What is the x-coordinate of the hole in the example given?

• 4

• -2

• 0

• 6

What is the y-coordinate of the hole in the example given?

• -1/3

• 1/6

• -1/6

• 0

What remains in the denominator after simplification indicates what feature of the graph?

• An x-intercept

• A horizontal asymptote

• A vertical asymptote

• A hole

What is the x-coordinate of the vertical asymptote in the example given?

• 6

• 0

• 4

• -2