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To solve the function \( f(x) = \sqrt{x + 3} + 4 \) and complete the table, we will evaluate \( f(x) \) for each value of \( x \) provided in the table.

### Step-by-Step Calculations:

1. **For \( x = -3 \):**
   \[
   f(-3) = \sqrt{-3 + 3} + 4 = \sqrt{0} + 4 = 0 + 4 = 4
   \]
   So, \( y = 4 \) when \( x = -3 \).

2. **For \( x = -2 \):**
   \[
   f(-2) = \sqrt{-2 + 3} + 4 = \sqrt{1} + 4 = 1 + 4 = 5
   \]
   So, \( y = 5 \) when \( x = -2 \).

3. **For \( x = 1 \):**
   \[
   f(1) = \sqrt{1 + 3} + 4 = \sqrt{4} + 4 = 2 + 4 = 6
   \]
   So, \( y = 6 \) when \( x = 1 \).

4. **For \( x = 6 \):**
   \[
   f(6) = \sqrt{6 + 3} + 4 = \sqrt{9} + 4 = 3 + 4 = 7
   \]
   So, \( y = 7 \) when \( x = 6 \).

### Completed Table:

| \( x \) | \( y = f(x) \) |
|:---:|:---:|
| -3  |  4  |
| -2  |  5  |
|  1  |  6  |
|  6  |  7  |

Would you like more details or have any questions?

Here are some related questions:
1. What happens to \( f(x) \) as \( x \) increases further?
2. How does the function \( f(x) = \sqrt{x + 3} + 4 \) behave for negative values of \( x \)?
3. What is the domain of the function \( f(x) = \sqrt{x + 3} + 4 \)?
4. How would the function change if the constant added outside the square root was different?
5. What is the range of \( f(x) = \sqrt{x + 3} + 4 \)?

**Tip:** When dealing with square root functions, always check that the expression under the square root is non-negative to ensure the function is defined.

Complete the table for the function f(x) = √(x + 3) + 4 with given values of x: -3, -2, 1, and 6.

Learn how to complete the table for the function f(x) = √(x + 3) + 4 by evaluating it for different values of x, including -3, -2, 1, and 6. This problem is suitable for students in Grades 8-10 and covers key algebraic concepts.

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