which is the graph of $f(x)=(2)^{-x}$?

Explanation:

Step1: Rewrite the function

The function $f(x)=(2)^{-x}$ can be rewritten as $f(x)=\left(\frac{1}{2}\right)^{x}$ using the negative - exponent rule $a^{-n}=\frac{1}{a^{n}}$.

Step2: Analyze the properties of exponential functions

For an exponential function of the form $y = a^{x}$, when $0\lt a\lt1$, the function is a decreasing function. Here $a=\frac{1}{2}$, so $y = f(x)$ is a decreasing function. Also, when $x = 0$, $y=\left(\frac{1}{2}\right)^{0}=1$.

Step3: Evaluate the function at some points

When $x = 1$, $y=\frac{1}{2}$; when $x=- 1$, $y = 2$.

Answer:

The graph that is a decreasing curve and passes through the point $(0,1)$ with $y -$ values getting smaller as $x$ increases is the correct graph. Among the given graphs, the third graph (from left - to - right) is the graph of $f(x)=(2)^{-x}$.