Finding the asymptotes

The video tutorial explains how to find vertical and horizontal asymptotes of a function. It begins with an introduction to asymptotes, followed by detailed steps to determine vertical asymptotes by setting the denominator of a rational function to zero. The tutorial then covers horizontal asymptotes, focusing on comparing the degrees and leading coefficients of polynomials. The video concludes with a brief mention of slant asymptotes, which will be covered in another video.

What is the primary method to find vertical asymptotes of a rational function?

• Find the derivative of the function

• Solve for x-intercepts

• Set the denominator equal to zero

• Set the numerator equal to zero

In the example provided, what are the vertical asymptotes for the equation X^2 = 3?

• X = 0

• X = ±sqrt(3)

• X = ±3

• X = ±1

When comparing polynomials to find horizontal asymptotes, what should you compare?

• The coefficients of the constant terms

• The degrees and leading coefficients

• The x-intercepts

• The y-intercepts

What is the horizontal asymptote when the degree of the numerator is less than the degree of the denominator?

• No horizontal asymptote

• y = 1

• y = x

• y = 0

How do you find the horizontal asymptote when the degrees of the numerator and denominator are equal?

• Subtract the coefficients

• Multiply the coefficients

• Divide the coefficients

• Add the coefficients

What happens to the horizontal asymptote when the degree of the numerator is greater than the degree of the denominator?

• y = x

• No horizontal asymptote

• y = 1

• y = 0

If the leading coefficients of the numerator and denominator are 3 and 4 respectively, what is the horizontal asymptote?

• y = 4/3

• y = 3/4

• y = 1

• y = 0