Question

Consider the function .

Which statement correctly describes the function’s behavior around its vertical asymptote?

As x → –2–, f(x) → ∞ and as x → –2+, f(x) → ∞.
As x → –2–, f(x) → –∞ and as x → –2+, f(x) → ∞.
As x → –2–, f(x) → –∞ and as x → –2+, f(x) → –∞.
As x → –2–, f(x) → ∞ and as x → –2+, f(x) → –∞.

Answer 1

The second statement is correct.

For f(x) = 1/(x+2) (vertical asymptote at x = −2): if x → −2− then x+2 is a small negative number so 1/(x+2) → −∞; if x → −2+ then x+2 is a small positive number so 1/(x+2) → +∞.