Identifying asymptotes Vertical and Horizontal

The video tutorial explains how to identify vertical and horizontal asymptotes in rational functions. It covers setting the denominator to zero to find vertical asymptotes and discusses the types of discontinuities, such as holes and asymptotes. The tutorial also explains simplifying expressions and determining horizontal asymptotes by comparing the degrees of the numerator and denominator. Additionally, it touches on cube roots and polynomial expressions.

What is the first step in identifying a vertical asymptote of a function?

• Integrate the function

• Find the derivative of the function

• Set the denominator equal to zero

• Set the numerator equal to zero

What distinguishes a hole from a vertical asymptote in a function?

• Holes are found in the numerator, asymptotes in the denominator

• Holes are removable discontinuities, asymptotes are not

• Holes occur at x = 0, asymptotes do not

• Holes are non-removable, asymptotes are removable

After factoring the numerator, what confirms the presence of a vertical asymptote?

• The numerator can be divided out

• The denominator can be divided out

• The numerator cannot be divided out

• The expression simplifies to zero

How do you determine the horizontal asymptote when the degree of the numerator is less than the degree of the denominator?

• There is no horizontal asymptote

• The horizontal asymptote is x = 0

• The horizontal asymptote is y = 0

• The horizontal asymptote is y = 1

What is the cube root of 8 in the context of determining asymptotes?

• 4

• 1

• 3

• 2