The Simple Way to Determine the Vertical and Slant Asymptotes

The video tutorial covers the concepts of X intercepts, factoring, and the differences between holes and asymptotes. It explains how to find vertical and horizontal asymptotes by comparing the degrees of the numerator and denominator. The tutorial also demonstrates how to find slant asymptotes using long division, emphasizing the importance of understanding these concepts for solving mathematical problems involving rational functions.

What happens to a term in a function when it can be factored out completely?

• It becomes a hole.

• It becomes a vertical line.

• It becomes an asymptote.

• It remains unchanged.

How do you determine the location of vertical asymptotes in a function?

• By setting the denominator equal to zero.

• By comparing the degrees of the numerator and denominator.

• By setting the numerator equal to zero.

• By factoring the numerator.

When does a function not have a horizontal asymptote?

• When the function is a constant.

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

What method is used to find a slant asymptote when there is no horizontal asymptote?

• Synthetic division

• Long division

• Completing the square

• Factoring

What is the significance of the remainder when finding a slant asymptote?

• It is used to find the y-intercept of the asymptote.

• It is not important for finding the slant asymptote.

• It determines the slope of the asymptote.

• It indicates the presence of a vertical asymptote.