1. **State the problem:** We have the function $f(x) = a^x + b$ with constants $a$ and $b$. The graph has an x-intercept at $(2,0)$ and a y-intercept at $(0,-323)$. We need to find the value of $b$. 2. **Use the intercepts to form equations:** - At the x-intercept $(2,0)$, $f(2) = 0$, so: $$a^2 + b = 0$$ - At the y-intercept $(0,-323)$, $f(0) = -323$, so: $$a^0 + b = -323$$ 3. **Simplify the y-intercept equation:** Since $a^0 = 1$, we have: $$1 + b = -323$$ 4. **Solve for $b$:** $$b = -323 - 1 = -324$$ 5. **Verify with the x-intercept equation:** Substitute $b = -324$ into $a^2 + b = 0$: $$a^2 - 324 = 0$$ $$a^2 = 324$$ $$a = \pm 18$$ Since $a$ is a base of an exponential function, it is positive, so $a = 18$. **Final answer:** $$b = -324$$