Answer
$f(x) = 1+tan~\frac{x}{2}$
Work Step by Step
We can see that this is the graph for a tangent function.
Compared with a standard tangent function, the first positive asymptote occurs at $x = \pi$ instead of $\frac{\pi}{2}$. Therefore we need to include the term $\frac{x}{2}$ for the angle in the function.
Compared with a standard tangent function, the y-values are translated upward by 1 unit. Therefore we need to include the term +1 in this function.
The equation for this graph is: $f(x) = 1+tan~\frac{x}{2}$
