https://file.aiquickdraw.com/mathbot/file/1726971232516aka43epk.jpg

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 \(x\).

Learn how to graph the square root function y = √x - 7. This guide includes key points such as domain, endpoint, and how to calculate other points on the graph. Suitable for students in Grades 8-10.

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