the function shown is f(x) = -3^x+2 - 1. as x approaches negative infinity, f(x) approaches what value…

the function shown is f(x) = -3^x+2 - 1. as x approaches negative infinity, f(x) approaches what value? negative infinity -2 infinity -1

the function shown is f(x) = -3^x+2 - 1. as x approaches negative infinity, f(x) approaches what value? negative infinity -2 infinity -1

Answer

Explanation:

Step1: Analyze the exponential part

As (x\to-\infty), consider (y = x + 2). Then (y\to-\infty) too. And (3^{x + 2}=3^y). As (y\to-\infty), (3^y=\frac{1}{3^{-y}}\to0) since (-y\to\infty) and the exponential - function (a^t) ((a>1)) grows without bound as (t\to\infty).

Step2: Find the limit of the function

We have (f(x)=-3^{x + 2}-1). Substituting the limit of (3^{x + 2}) as (x\to-\infty) into the function. (\lim_{x\to-\infty}f(x)=-\lim_{x\to-\infty}3^{x + 2}-1). Since (\lim_{x\to-\infty}3^{x + 2}=0), then (\lim_{x\to-\infty}f(x)=-0 - 1=-1).

Answer:

-1