https://file.aiquickdraw.com/mathbot/file/1730348917201d0ax9jfh.jpg

The function given is:

\[
f(x) = \sqrt{x + 4}
\]

### Step 1: Determine the Domain
Since this is a square root function, the expression under the square root, \( x + 4 \), must be non-negative:
\[
x + 4 \geq 0 \Rightarrow x \geq -4
\]
Thus, the domain of \( f(x) \) is \( x \geq -4 \).

### Step 2: Identify Key Points
The problem asks for four points: the leftmost point and three additional points. Let's choose values of \( x \) within the domain:

1. **Leftmost point**: \( x = -4 \)
   \[
   f(-4) = \sqrt{-4 + 4} = \sqrt{0} = 0
   \]
   So, one point is \( (-4, 0) \).

2. **Next point**: \( x = 0 \)
   \[
   f(0) = \sqrt{0 + 4} = \sqrt{4} = 2
   \]
   Another point is \( (0, 2) \).

3. **Next point**: \( x = 5 \)
   \[
   f(5) = \sqrt{5 + 4} = \sqrt{9} = 3
   \]
   This gives the point \( (5, 3) \).

4. **Next point**: \( x = 9 \)
   \[
   f(9) = \sqrt{9 + 4} = \sqrt{13} \approx 3.6
   \]
   This point is approximately \( (9, 3.6) \).

### Step 3: Plot the Points
On the graph, plot these points:

- \( (-4, 0) \)
- \( (0, 2) \)
- \( (5, 3) \)
- \( (9, 3.6) \)

These points represent the curve of \( f(x) = \sqrt{x + 4} \). The function will start at \( (-4, 0) \) and increase gradually to the right as \( x \) increases.

Would you like more details on graphing techniques or the function's behavior? 

### Additional Questions for Further Exploration:
1. How would the graph change if the function were \( f(x) = \sqrt{x - 4} \)?
2. What is the range of the function \( f(x) = \sqrt{x + 4} \)?
3. How would you determine the inverse of \( f(x) = \sqrt{x + 4} \)?
4. How do transformations affect the graph of a square root function?
5. How can you use this function to model real-world situations?

#### Tip:
When working with square root functions, always check the domain since square roots are only defined for non-negative values inside the radical.

Graph the function f(x) = √(x + 4) and plot four points on the graph: the leftmost point and three additional points.

Learn how to graph the square root function f(x) = √(x + 4) with a detailed solution. This problem covers key concepts such as domain, range, and plotting points, making it ideal for students in Grades 9-10.

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