2) what is the asymptote of (f(x)=(0.2)^x)? a.the (x)-axis ((y = 0)) b.the (y)-axis ((x = 0)) c.the line (x…

Answer:

A. The x - axis ($y = 0$)

Explanation:

Step1: Recall exponential - function form

The general form of an exponential function is $y = a\cdot b^{x}$, where in $y=(0.2)^{x}$, $a = 1$ and $b=0.2$ ($0 < b<1$).

Step2: Analyze the limit as $x\rightarrow\infty$

We find $\lim_{x\rightarrow\infty}(0.2)^{x}$. Since $0 < 0.2<1$, as $x$ gets larger and larger, $(0.2)^{x}$ approaches 0.

Step3: Determine the asymptote

The function $y=(0.2)^{x}$ gets closer and closer to the line $y = 0$ as $x\rightarrow\infty$. So the horizontal asymptote is the x - axis, which is represented by the equation $y = 0$.