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.