https://file.aiquickdraw.com/mathbot/file/1730300275275g043dzi4.jpg

Let's analyze the graph and address each question:

### Questions Breakdown:

1. **(a) For what value(s) of \( x \) does the function obtain a relative minimum?**
   - From the graph, we can see that the function has a relative minimum at \( x = -11 \), where the value is \( y = -9 \). This is a local low point in the graph.

   So, the answer to (a) would be:
   - **The function obtains a relative minimum at \( x = -11 \).**

2. **(b) Find the relative minimum value.**
   - The relative minimum value occurs at \( y = -9 \) at \( x = -11 \).

   The answer to (b) is:
   - **The relative minimum value is \( -9 \).**

3. **(c) For what value(s) of \( x \) does the function obtain a relative maximum?**
   - The graph shows a relative maximum at \( x = -7 \), where the value is \( y = 7 \). Another local high point is also present at \( x = 2 \) with \( y = 1 \).

   So, the answer to (c) is:
   - **The function obtains relative maximums at \( x = -7 \) and \( x = 2 \).**

4. **(d) Find the relative maximum value.**
   - The highest relative maximum value observed is \( y = 7 \) at \( x = -7 \).

   Therefore, the answer to (d) is:
   - **The relative maximum value is \( 7 \).**

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Would you like more details on any specific part? Here are related questions you might find helpful:

1. How can you determine relative minima and maxima from a graph without specific coordinates?
2. What is the difference between absolute and relative extrema?
3. How does the first derivative test help in finding relative extrema?
4. Can relative extrema exist on endpoints of a function's interval?
5. How can concavity affect the number and location of relative extrema?

**Tip:** When analyzing a graph, observe points where the function changes direction to find relative minima and maxima.

For what values of x does the function obtain a relative minimum? Find the relative minimum value. For what values of x does the function obtain a relative maximum? Find the relative maximum value.

Learn how to find relative minimum and maximum values of a function by analyzing its graph. This problem explores calculus concepts, including local extrema and graph analysis, suitable for students in Grades 11-12.

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