Rational Functions and Asymptotes

This lesson covers rational functions, focusing on finding domains, vertical, horizontal, and slant asymptotes. It explains how to determine vertical asymptotes by setting the denominator to zero and solving, and how horizontal asymptotes depend on the degrees of the numerator and denominator. Slant asymptotes are identified when the numerator's degree exceeds the denominator's by one, using long division. Examples are provided to illustrate these concepts, and Desmos is used for verification.

What is the primary focus of the lesson on rational functions?

• Finding the domain, asymptotes, and graphing rational functions

• Finding the range of rational functions

• Understanding polynomial functions

• Solving linear equations

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

• Set the numerator equal to zero

• Set the denominator equal to zero

• Find the intersection of the function with the x-axis

• Find the intersection of the function with the y-axis

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

• There is no horizontal asymptote

• The horizontal asymptote is y = 0

• The horizontal asymptote is y = n/m

• There is a vertical asymptote

When does a slant asymptote occur?

• When the degree of the denominator is greater than the numerator by exactly one

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

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

• When the degree of the numerator is greater than the denominator by exactly one

How do you find the domain of a rational function?

• By finding the x-intercepts

• By setting the denominator equal to zero and solving

• By setting the numerator equal to zero

• By finding the y-intercepts

What should you watch out for when finding vertical asymptotes?

• Common factors in the numerator and denominator

• The degree of the numerator

• The x-intercepts of the function

• The degree of the denominator

What is the horizontal asymptote when the degrees of the numerator and denominator are equal?

• y = 0

• y = n/m

• y = x

• There is no horizontal asymptote

What is the horizontal asymptote when the degree of the numerator is less than the denominator?

• y = x

• There is no horizontal asymptote

• y = 0

• y = n/m

How do you find a slant asymptote?

• By finding the x-intercepts

• By setting the numerator equal to zero

• By setting the denominator equal to zero

• By performing long division

What is another name for a slant asymptote?

• Oblique asymptote

• Horizontal asymptote

• Vertical asymptote

• Curved asymptote