Question 85bda40c

The function $f$ is defined by $f\left(x\right)=a^x+b$, where $a$ and $b$ are constants. In the $xy$-plane, the graph of $y=f\left(x\right)$ has an $x$-intercept at $\left(2,0\right)$ and a $y$-intercept at $\left(0,-323\right)$. What is the value of $b$?