Vertical Asymptotes (8.5.1)

Question 1

What are asymptotes?

Answer 1

• Asymptotes are lines that the graph of a function approaches. A vertical asymptote to the graph of a function f is a line whose equation is x = a, where lim x -> a+ f(x) = ±∞, or lim x-> a- f(x) = ±∞.

Question 2

How do you identify vertical asymptotes?

Answer 2

• Identify vertical asymptotes for a rational function by factoring the numerator and denominator, canceling where possible, and determining where the resulting denominator is zero.

Question 3

How can you tell if there may be a hole at a certain point?

Answer 3

• If a given point makes both the numerator and denominator of a function equal zero, then there might be a hole in the graph of the function at that point.