Identify any horizontal or vertical asypmtotes of a rational function

The video tutorial explains how to determine horizontal and vertical asymptotes of rational functions. It begins with identifying horizontal asymptotes using exponent rules and the horizontal asymptote test. Then, it moves on to finding vertical asymptotes by setting the denominator equal to zero and solving for the values that make it zero, which are excluded from the domain. The tutorial concludes with a brief discussion on the domain of the function, emphasizing that it includes all real numbers except where the vertical asymptotes occur.

What is the horizontal asymptote of a rational function if the degree of the numerator is less than the degree of the denominator?

• The horizontal asymptote is at y = 0.

• There is no horizontal asymptote.

• The horizontal asymptote is at y = 1.

• The horizontal asymptote is at y = infinity.

How do you determine the vertical asymptotes of a rational function?

• By setting the entire function equal to zero.

• By comparing the degrees of the numerator and denominator.

• By finding the values that make the denominator zero.

• By setting the numerator equal to zero.

Which of the following is NOT a step in finding vertical asymptotes?

• Solving for the values of x.

• Taking the square root of the numerator.

• Excluding the found values from the domain.

• Setting the denominator equal to zero.

What happens to the domain of a function at the vertical asymptotes?

• The domain includes the vertical asymptotes.

• The domain excludes the vertical asymptotes.

• The domain is unaffected by the vertical asymptotes.

• The domain is only the vertical asymptotes.

If a rational function has a vertical asymptote at x = 2, what is true about the function's domain?

• The domain is only x = 2.

• The domain includes x = 2.

• The domain excludes x = 2.

• The domain is all real numbers.