Graphing Basic and Complex Rational Functions

The video tutorial covers graphing rational functions, focusing on the parent rational function y = 1/x. It introduces the AIM acronym for graphing: Asymptotes, Intercepts, and Multiplicity. The tutorial explains how to find vertical and horizontal asymptotes, x and y intercepts, and discusses multiplicity in rational functions. It provides examples of graphing rational functions and addresses the concept of holes in these functions.

What is the parent rational function?

• y = 1/x^2

• y = x

• y = 1/x

• y = x^2

What does the 'A' in the AIM acronym stand for?

• Asymptotes

• Axes

• Angles

• Areas

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

• Set the entire function equal to zero

• Set the numerator equal to zero

• Set the denominator equal to zero

• Set the numerator and denominator equal to zero

When the degree of the denominator is higher than the numerator, what is the horizontal asymptote?

• y = 1

• y = x

• y = 0

• y = infinity

What does the 'I' in the AIM acronym stand for?

• Intercepts

• Intervals

• Inverses

• Integrals

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

• Set the numerator equal to zero

• Set the denominator equal to zero

• Set the entire function equal to zero

• Set the numerator and denominator equal to zero

What does the 'M' in the AIM acronym stand for?

• Median

• Mean

• Multiplicity

• Magnitude

What is multiplicity in the context of rational functions?

• The number of times a factor repeats

• The number of terms in the function

• The number of intercepts

• The number of asymptotes

What happens to the graph of a function when there is multiplicity in the denominator?

• The function will have no intercepts

• The function will cross the asymptote

• The function will meet at the asymptote

• The function will have a double root bounce

What is a hole in a rational function?

• A point where the function is undefined

• A point where the function crosses the x-axis

• A point where the function crosses the y-axis

• A point where the function has an asymptote