To determine which graph represents the function $f(x) = 2^{-x}$, we need to understand its characteristics:

Characteristics of $f(x) = 2^{-x}$:

1. Base of the Exponent: The base of the exponent is $2$, and the exponent is $-x$, meaning it is a decreasing exponential function.
2. Domain: The domain is $(-\infty, \infty)$, as any real number $x$ is valid.
3. Range: Since the exponential function never reaches zero but approaches it asymptotically, the range is $(0, \infty)$.
4. Key Points:
   • At $x = 0$, $f(0) = 2^{0} = 1$.
   • At $x = 1$, $f(1) = 2^{-1} = \frac{1}{2}$.
   • At $x = -1$, $f(-1) = 2^{1} = 2$.
5. Asymptote: The graph has a horizontal asymptote at $y = 0$.

Comparing the Graphs:

• Look for a graph that decreases from left to right.
• Ensure the $y$-values at the key points match: $(0, 1), (1, \frac{1}{2}), (-1, 2)$.
• The graph must approach the $x$-axis but never touch it, indicating the horizontal asymptote.

Can you upload the graphs so we can identify the correct one together?