Question d3ef8ffa

The function $f$ is defined by $f\left(x\right)=a^x+b$, where $a$ and $b$ are constants and $a>0$. In the xy-plane, the graph of $y=f\left(x\right)$ has a y-intercept at $\left(0,-25\right)$ and passes through the point $\left(2,23\right)$. What is the value of $a+b$?