1. **State the problem:** We are given the function $$y = \sqrt{x} - 5 - 3$$ and a starting point $(5, -3)$. We want to understand the graph of this function. 2. **Rewrite the function:** Simplify the expression: $$y = \sqrt{x} - 5 - 3 = \sqrt{x} - 8$$ 3. **Understand the domain:** Since $y$ involves $\sqrt{x}$, the domain is $x \geq 0$ because the square root of a negative number is not real. 4. **Evaluate the function at the starting point $x=5$:** $$y = \sqrt{5} - 8$$ Calculate $\sqrt{5} \approx 2.236$: $$y \approx 2.236 - 8 = -5.764$$ 5. **Check the given point $(5, -3)$:** The function value at $x=5$ is approximately $-5.764$, which does not match $-3$. So $(5, -3)$ is not on the graph of $y = \sqrt{x} - 8$. 6. **Graph shape:** - The graph starts at $(0, -8)$ because $\sqrt{0} = 0$. - It increases slowly as $x$ increases because $\sqrt{x}$ grows slowly. - The graph is shifted down by 8 units compared to $y=\sqrt{x}$. 7. **Summary:** The function is $y = \sqrt{x} - 8$ with domain $x \geq 0$. The point $(5, -3)$ is not on this graph. **Final answer:** $$y = \sqrt{x} - 8$$