Find the Vertical, Horizontal and Slant Asymptote

The video tutorial covers how to find X and Y intercepts, vertical, horizontal, and slant asymptotes of a rational function. It explains that the X intercept does not exist due to imaginary roots, while the Y intercept is found by setting X to zero. Vertical asymptotes are determined by setting the denominator to zero. The tutorial also discusses the absence of horizontal asymptotes and the presence of a slant asymptote, which is calculated using synthetic division.

What is the condition for finding the X intercept of a function?

• Set y = 0

• Set the numerator to 0

• Set x = 0

• Set the denominator to 0

How do you determine the Y intercept of a function?

• Set the numerator to 0

• Set the denominator to 0

• Set y = 0

• Set x = 0

What must be true for a vertical asymptote to exist?

• The numerator must be zero

• The denominator must be zero

• The degrees of numerator and denominator must be equal

• The function must be linear

When does a horizontal asymptote not exist?

• When the function is linear

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

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

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

What is the difference in degrees between the numerator and denominator for a slant asymptote to exist?

• 2

• 1

• 3

• 0

Which method can be used to find a slant asymptote when the polynomial is in the form of x - k?

• Synthetic division

• Long division

• Completing the square

• Factoring

What role does the remainder play in finding a slant asymptote?

• It is part of the asymptote

• It is ignored

• It is added to the numerator

• It determines the slope