Question

Consider the function 𝑓⁡(𝑥) =𝑒𝑥−2 +1. Which statement(s) describe the end behavior of the function? Select all that apply.

Multiple select question.

A)
As 𝑥 →−∞, 𝑓⁡(𝑥) →−∞.


B)
As 𝑥 →−∞, 𝑓⁡(𝑥) →1.


C)
As 𝑥 →−∞, 𝑓⁡(𝑥) →∞


D)
As 𝑥 →∞, 𝑓⁡(𝑥) →−∞.


E)
As 𝑥 →∞, 𝑓⁡(𝑥) →1.


F)
As 𝑥 →∞, 𝑓⁡(𝑥) →∞.

Answer 1

Correct choices: B and F.

Reason: f(x) = e^{x-2} + 1. As x → −∞, e^{x-2} → 0 so f(x) → 1 (horizontal asymptote y = 1). As x → ∞, e^{x-2} → ∞ so f(x) → ∞.