Set 14: Exponential Functions (Advanced)

Choice A is correct. Choice A is the correct answer. The horizontal asymptote is determined by the constant term. 1. Standard Form: $f(x) = ab^x + k$, where $k$ is the vertical shift. 2. Asymptote: As $x \to -\infty$, $(2)^x \to 0$, so $f(x) \to 0 + 3 = 3$. 3. Conclusion: The horizontal asymptote is $y = 3$. Strategic Tip: The constant added/subtracted shifts the asymptote from $y=0$ to $y=k$. Choice B is incorrect because 5 is the coefficient $a$, not the asymptote. Choice C is incorrect because this would be true only if there were no constant term. Choice D is incorrect because 2 is the base, not related to the asymptote.