The function you need to graph is:

$y = \sqrt{x} - 7$

Key Points to Consider for Graphing:

1. Domain: The square root function $\sqrt{x}$ is only defined for non-negative values of $x$, so the domain of the function is $x \geq 0$.

2. Endpoint: The graph will start at $x = 0$, where: $y = \sqrt{0} - 7 = -7$ So, the point $(0, -7)$ is the starting point (endpoint) of the graph.

3. Other Points: To find additional points, choose positive values of $x$ and calculate $y$. For example:

   • When $x = 1$: $y = \sqrt{1} - 7 = 1 - 7 = -6$ So the point is $(1, -6)$.
   • When $x = 4$: $y = \sqrt{4} - 7 = 2 - 7 = -5$ So the point is $(4, -5)$.
   • When $x = 9$: $y = \sqrt{9} - 7 = 3 - 7 = -4$ So the point is $(9, -4)$.

Steps to Graph:

1. Start by plotting the point $(0, -7)$, which is the endpoint.
2. Plot the other calculated points: $(1, -6)$, $(4, -5)$, and $(9, -4)$.
3. Draw a smooth curve through these points, making sure the graph starts at $(0, -7)$ and gradually increases as $x$ increases.

Let me know if you want more details or have any questions!

Related Questions:

1. How would the graph change if the function were $y = \sqrt{x} + 7$?
2. What would the graph look like if the function were $y = -\sqrt{x} - 7$?
3. How does the square root transformation affect the shape of the graph compared to a linear graph?
4. What is the range of the function $y = \sqrt{x} - 7$?
5. How would you reflect this graph across the x-axis?

Tip:

When working with square root functions, remember that they are always increasing and only defined for non-negative values of $x$.