Set 12: Exponential Functions (Advanced)

Choice A is correct. Choice A is the correct answer. The asymptote comes from the vertical shift. 1. Form: $g(x) = ab^x + k$ where $k = -10$. 2. As $x \to \infty$: $(0.75)^x \to 0$, so $g(x) \to 0 - 10 = -10$. 3. Asymptote: $y = -10$. Strategic Tip: The constant term added/subtracted determines the horizontal asymptote. Choice B is incorrect because 80 is the coefficient, not the asymptote. Choice C is incorrect because 0.75 is the base. Choice D is incorrect because this ignores the $-10$ shift.