Question 1

What are vertical asymptotes?

Accepted Answer

Vertical asymptotes are vertical lines that a function approaches as the input approaches a certain value, where the function itself becomes infinite.

Question 2

How do you find vertical asymptotes?

Accepted Answer

Find vertical asymptotes by setting the denominator of a rational function to zero and solving for the variable.

Question 3

Why do vertical asymptotes occur?

Accepted Answer

They occur when a function becomes undefined due to division by zero, causing the function to increase or decrease without bound.

Question 4

Can a function cross a vertical asymptote?

Accepted Answer

No, a function cannot cross a vertical asymptote because it represents a point of undefined behavior or infinite value.

Question 5

What is the difference between vertical and horizontal asymptotes?

Accepted Answer

Vertical asymptotes occur at specific values of $$x$$ where the function becomes infinite, while horizontal asymptotes describe the behavior of a function as $$x$$ approaches infinity.