The graph in the image represents a piecewise function. Here's how the function can be expressed based on the graph:

1. From $x = -\infty$ to $x = 1$, the graph shows a horizontal line at $y = 3$. However, at $x = 1$, there is an open circle, indicating that the function is not defined at $x = 1$.

   Thus, for $x < 1$, the function is: $f(x) = 3 \quad \text{for} \quad x < 1$

2. At $x = 1$, the function has a closed dot at $y = 5$, indicating that the value of the function at this point is 5.

   Therefore: $f(x) = 5 \quad \text{for} \quad x = 1$

3. For $x > 1$, the graph continues with a horizontal line at $y = 3$, meaning the function returns to the value 3 for all $x > 1$.

   Hence, for $x > 1$: $f(x) = 3 \quad \text{for} \quad x > 1$

Complete Piecewise Function: