Question

3
select the correct graph.
which graph represents function f?
f(x) = (1/3)^x

Explanation:

Step1: Analyze exponential - function form

The general form of an exponential function is $y = a^x$, where $a>0,a
eq1$. When $0 < a<1$, the function $y = a^x$ is a decreasing exponential function. In the function $f(x)=(\frac{1}{3})^x$, $a = \frac{1}{3}$ and $0<\frac{1}{3}<1$, so $f(x)$ is a decreasing function.

Step2: Find the y - intercept

When $x = 0$, $f(0)=(\frac{1}{3})^0=1$. So the function $f(x)$ passes through the point $(0,1)$.

Step3: Analyze the end - behavior

As $x
ightarrow+\infty$, $f(x)=(\frac{1}{3})^x
ightarrow0$. As $x
ightarrow-\infty$, $f(x)=(\frac{1}{3})^x
ightarrow+\infty$.

Answer:

The graph that is decreasing, passes through the point $(0,1)$ and approaches the $x$ - axis as $x$ goes to positive infinity is the correct graph. (Since the actual graphs are not labeled, you need to identify the graph with these characteristics among the given options).