https://file.aiquickdraw.com/mathbot/file/1727102121417os1c86do.jpg

Let's go through the questions one by one based on the image provided:

1. **Domain:**
   - The graph shows two vertical asymptotes at \( x = 2 \) and \( x = -2 \), meaning the function is undefined at these points. The domain consists of all real numbers except \( x = 2 \) and \( x = -2 \). 
   - So, the domain inequality is: 
     \[
     x \neq 2 \quad \text{and} \quad x \neq -2
     \]

2. **Range:**
   - From the graph, the horizontal asymptote is \( y = 0 \), meaning the function never takes the value \( y = 0 \). The function covers all other real values for \( y \), except \( y = 0 \).
   - The range inequality is: 
     \[
     y \neq 0
     \]

3. **Function Evaluation \( f(x) = \sqrt{x + 9} \):**
   - To find \( f(-4) \), substitute \( x = -4 \) into the given function:
     \[
     f(-4) = \sqrt{-4 + 9} = \sqrt{5}
     \]
     - You can leave the answer as \( \sqrt{5} \) or approximate it to three significant figures:
     \[
     \sqrt{5} \approx 2.236
     \]

Let me know if you'd like any details or further clarification.

### Additional Questions:
1. What is the domain of a function with a square root in its expression?
2. How does a vertical asymptote affect the domain of a function?
3. Can a function have more than one asymptote? Explain with an example.
4. How is the range of a function determined from its graph?
5. What are the properties of square root functions, and how do they affect the domain and range?

### Tip:
When evaluating square root functions, ensure the value under the square root is non-negative to keep the function real-valued.

1. Write down the domain as an inequality in the form of x ≠ a. 2. Write down the range as an inequality in the form of y ≠ b. 3. If f(x) = √(x + 9), find f(-4).

Learn how to find the domain and range of a function involving asymptotes, and evaluate square root functions. Example provided: find f(-4) for f(x) = √(x + 9), suitable for students in Grades 9-12.

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