Exploring Graphs of Rational Functions with Vertical Asymptotes

The video tutorial covers the second day of graphing rational functions, focusing on functions with vertical asymptotes, horizontal asymptotes, and intercepts. It explains the AIM method for graphing, which includes identifying asymptotes, intercepts, and multiplicity. The tutorial also addresses common misconceptions about asymptotes and demonstrates how to solve problems involving rational functions with holes. Advanced graphing techniques are discussed, providing a comprehensive understanding of rational functions.

What is the first step in graphing a rational function?

• Graph the vertical asymptote

• Identify the horizontal asymptote

• Factor the numerator and denominator

• Find the x-intercept

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

• Find the highest exponent in the numerator

• Set the denominator equal to zero

• Find the highest exponent in the denominator

• Set the numerator equal to zero

What is the horizontal asymptote for a rational function where the degree of the numerator is less than the degree of the denominator?

• x = 1

• x = 0

• y = 0

• y = 1

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

• Set the numerator equal to zero

• Find the highest exponent in the numerator

• Set the denominator equal to zero

• Find the highest exponent in the denominator

What does multiplicity in the numerator indicate?

• The function will meet at the vertical asymptote

• The function will have a hole

• The function will have a double root bounce at the x-intercept

• The function will cross the horizontal asymptote

What is the behavior of a function between two vertical asymptotes if there is no multiplicity?

• The function will cross the horizontal asymptote

• The function will meet at the vertical asymptotes

• The function will not meet at the vertical asymptotes

• The function will have a hole

How do you identify the location of a hole in a rational function?

• Find the highest exponent in the numerator

• Find the common factor in the numerator and denominator and set it equal to zero

• Set the denominator equal to zero

• Set the numerator equal to zero

What is the horizontal asymptote for a rational function where the degrees of the numerator and denominator are the same?

• y = the sum of the leading coefficients

• y = 0

• y = 1

• y = the ratio of the leading coefficients

What does multiplicity in the denominator indicate?

• The function will cross the horizontal asymptote

• The function will have a double root bounce at the x-intercept

• The function will have a hole

• The function will meet at the vertical asymptote

How can you verify the graph of a rational function?

• By using a graphing calculator or graphing software

• By finding the y-intercept

• By finding the x-intercept

• By identifying the vertical asymptote