Vertical and Horizontal Asymptotes

The video tutorial explains how to analyze a rational function by determining its y-intercept, x-intercepts, vertical asymptotes, and horizontal asymptote. It begins with factoring the function, then uses these forms to find intercepts and asymptotes. The tutorial also discusses the significance of the degrees of the numerator and denominator in identifying horizontal asymptotes.

What is the first step in factoring a rational function?

• Calculating the y-intercept

• Identifying the degree of the numerator

• Setting the function equal to zero

• Finding the common factor of the numerator and denominator

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

• Set y equal to zero

• Set x equal to zero

• Find the zeros of the denominator

• Use the factored form only

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

• (0, 1/6)

• (0, -1/6)

• (1/3, 0)

• (-2, 0)

To find the x-intercepts, what must be true about the rational function?

• The numerator must be zero

• The function must be undefined

• Both numerator and denominator must be zero

• The denominator must be zero

What are the x-intercepts of the rational function?

• (1/3, 0) and (-2, 0)

• (-3, 0) and (-4/3, 0)

• (0, 0) and (1, 0)

• (0, -1/6) and (1/3, 0)

What condition must be met for a vertical asymptote to exist?

• The function must be continuous

• The numerator must be zero

• The denominator must be zero

• Both numerator and denominator must be zero

What are the vertical asymptotes of the rational function?

• x = -3 and x = -4/3

• x = 1/3 and x = -2

• x = 0 and x = 1

• x = 3 and x = 4/3

How is the horizontal asymptote determined when the degrees of the numerator and denominator are the same?

• By the difference of the coefficients

• By the product of the coefficients

• By the sum of the coefficients

• By the ratio of the leading coefficients

What is the horizontal asymptote of the rational function?

• y = -1

• y = 1

• y = 0

• y = 3

What happens to the function value if the degree of the numerator is higher than the denominator?

• The function value approaches zero

• The function value remains constant

• The function value decreases without bound

• The function value increases without bound