How to find the vertical and horizontal asymptotes of a rational function

The video tutorial explains the concepts of non-removable and removable discontinuities, focusing on asymptotes and holes. It demonstrates how to factor numerators and denominators to identify these discontinuities. The tutorial further distinguishes between vertical asymptotes and holes, and explains how to find horizontal asymptotes by comparing the degrees of the numerator and denominator.

What is the main difference between a removable and a non-removable discontinuity?

• Both can be factored out, but only removable discontinuities affect the numerator.

• Neither can be factored out, but they affect the graph differently.

• A non-removable discontinuity can be factored out, while a removable cannot.

• A removable discontinuity can be factored out, while a non-removable cannot.

How do you determine if a discontinuity is a hole?

• If the factor does not appear in either the numerator or denominator.

• If the factor only appears in the denominator.

• If the factor cancels out in both the numerator and denominator.

• If the factor only appears in the numerator.

What is the vertical asymptote in the given example?

• x = 4

• x = 1

• x = -4

• x = 0

When is y = 0 the horizontal asymptote?

• When the degrees of both numerator and denominator are zero.

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

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

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

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

• The horizontal asymptote is determined by the leading coefficients.

• The horizontal asymptote is y = 1.

• There is no horizontal asymptote.

• The horizontal asymptote is y = 0.