Question

question 24 of 42
which of the following is the best definition of a vertical asymptote?
a. a horizontal line that the graph of a function approaches and intersects
b. a vertical line that the graph of a function approaches but never intersects
c. a vertical line that the graph of a function approaches and intersects
d. a horizontal line that the graph of a function approaches but never intersects

Explanation:

To determine the best definition of a vertical asymptote, we analyze each option:

• Option A: A vertical asymptote is not horizontal, and the graph does not intersect it, so A is incorrect.
• Option B: A vertical asymptote is a vertical line that the function's graph approaches but never intersects (due to the function being undefined at that x - value or having infinite behavior), so this matches the definition.
• Option C: The graph of a function does not intersect its vertical asymptote, so C is incorrect.
• Option D: This describes a horizontal asymptote, not a vertical one, so D is incorrect.

Answer:

B. A vertical line that the graph of a function approaches but never intersects