Exploring Intercepts and Asymptotes of Rational Functions

The video tutorial explains how to analyze a rational function by determining its y-intercept, x-intercepts, vertical asymptotes, and horizontal asymptotes. It begins with factoring the numerator and denominator, then proceeds to find the y-intercept by setting x to zero. The x-intercepts are found by setting the numerator to zero, provided there are no common factors with the denominator. Vertical asymptotes are determined by setting the denominator to zero, and horizontal asymptotes are identified by comparing the degrees of the numerator and denominator. The tutorial concludes with graphing the function to verify the results.

What is the first step in analyzing a rational function?

• Graphing the function

• Determining the horizontal asymptote

• Factoring the numerator and denominator

• Finding the y-intercept

What are the factors of the numerator 2x^2 - 9x - 5?

• (2x + 1)(x - 5)

• (2x - 1)(x + 5)

• (2x + 5)(x - 1)

• (2x - 5)(x + 1)

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

• Set the numerator equal to zero

• Set x = 0

• Set the denominator equal to zero

• Set y = 0

What is the y-intercept of the given rational function?

• (5/3, 0)

• (0, -5/3)

• (-5/3, 0)

• (0, 5/3)

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

• Set the denominator equal to zero

• Set the numerator equal to zero

• Set x = 0

• Set y = 0

What are the x-intercepts of the given rational function?

• (1/2, 0) and (5, 0)

• (-1/2, 0) and (-5, 0)

• (1/2, 0) and (-5, 0)

• (-1/2, 0) and (5, 0)

How do you determine the vertical asymptotes of a rational function?

• Set x = 0

• Set the numerator equal to zero

• Set the denominator equal to zero

• Set y = 0

What are the vertical asymptotes of the given rational function?

• x = 1/2 and x = -3

• x = -1/2 and x = 3

• x = -1/2 and x = -3

• x = 1/2 and x = 3

What is the horizontal asymptote of the given rational function?

• y = 1

• y = 0

• y = -1

• y = 2

What does the graph of the function verify?

• The y-intercept is incorrect

• The function has no asymptotes

• The x-intercepts are incorrect

• The vertical and horizontal asymptotes are correct