The problem asks to find the graph of the function $f(x) = 0.5^x$. This is an exponential function of the form $a^x$ where $a = 0.5$.

1. Problem Description

The problem asks to find the graph of the function $f(x) = 0.5^x$. This is an exponential function of the form $a^x$ where $a = 0.5$.

2. Solution Steps

Since the function is $f(x) = 0.5^x = (1/2)^x$, it's an exponential function with a base between 0 and

1. Exponential functions of the form $y = a^x$ have different behavior based on the value of $a$.

- If $a > 1$, the function is increasing.

- If $0 < a < 1$, the function is decreasing.

Also, all exponential functions of this form pass through the point (0, 1) because $a^0 = 1$.

As $x$ approaches positive infinity, $0.5^x$ approaches

0. As $x$ approaches negative infinity, $0.5^x$ approaches positive infinity.

Based on these characteristics, the graph should:

- Pass through the point (0, 1).

- Be decreasing.

- Approach 0 as x goes to infinity.

- Approach infinity as x goes to negative infinity.

3. Final Answer

The graph is a decreasing exponential function that passes through (0,1) and approaches the x-axis as x goes to infinity. (Without the picture options, it is impossible to pick a specific graph).