https://file.aiquickdraw.com/mathbot/file/1726109578562imwg2bqb.jpg

Let's work through each part of the problem based on the graph.

1. **\( f(-6) \)**: 
   To find \( f(-6) \), locate \( x = -6 \) on the graph. At \( x = -6 \), the function value (y-value) is 3. Therefore:
   \[
   f(-6) = 3
   \]

2. **When \( f(x) = 2 \)**:
   We need to find the x-value where the function \( f(x) = 2 \). By observing the graph, \( f(x) = 2 \) occurs at \( x = 0 \). Therefore:
   \[
   \text{When } x = 0, \ f(x) = 2
   \]

3. **The domain**:
   The domain is the set of all x-values for which the function is defined. From the graph, the function starts at \( x = -10 \) and ends at \( x = 5 \). So, the domain is:
   \[
   \text{Domain} = [-10, 5]
   \]
   (Note that both ends of the domain include the endpoints, since the function is defined at \( x = -10 \) and \( x = 5 \)).

4. **Is the function one-to-one?**:
   A function is one-to-one if each x-value has a unique y-value, and no y-value is repeated. From the graph, the function is not one-to-one because, for example, \( f(-6) = 3 \) and \( f(-10) = 3 \). Since there are multiple x-values corresponding to the same y-value, the function is **not one-to-one**. So:
   \[
   \text{Answer: No}
   \]

Would you like more details on any part of this?

Here are 5 related questions for further practice:
1. What is the range of this function?
2. Determine \( f(3) \) based on the graph.
3. Find the x-value where \( f(x) = 4 \).
4. Is the function continuous on its domain? Explain.
5. Does the function have any symmetry (e.g., even, odd, or neither)?

**Tip:** Always check both the x- and y-values when analyzing a function's domain and range from its graph.

Answer the following statements about the function f(x). Find f(-6), the x-value where f(x) = 2, the domain, and determine if the function is one-to-one.

Learn how to analyze the function f(x) using its graph. This problem includes finding f(-6), identifying when f(x) = 2, determining the domain, and deciding if the function is one-to-one. Suitable for high school students.

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