Set 7: Exponential Functions (Advanced)

Choice A is correct. Choice A is the correct answer. Analyze the limit as $x \to -\infty$. 1. Negative Exponent: As $x \to -\infty$, $(3)^x = \frac{1}{3^{|x|}} \to 0$. 2. Function: $f(x) = 100(3)^x \to 100(0) = 0$. 3. Asymptote: The horizontal asymptote is $y = 0$ (x-axis). Strategic Tip: For exponential growth ($b > 1$), the function approaches 0 as $x \to -\infty$. Choice B is incorrect because 100 is the value at $x=0$, not the limit. Choice C is incorrect because 3 is the base. Choice D is incorrect because the function approaches 0, not $-\infty$.