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Determine the range of the following graph and put it in alternate notation:

To determine the range of the function based on the graph, we need to observe the minimum and maximum values on the \( y \)-axis that the curve reaches.

### Analysis:
- The graph starts at approximately \( y = -3 \) on the left-hand side, going up to a maximum of around \( y = 9 \).
- Then, it decreases down to a minimum value of \( y = -5 \) before increasing again towards \( y = 6 \).

### Range in Interval Notation:
- The curve appears to reach the points \( (-11, -3) \), \( (-6, 9) \), \( (3, -5) \), and \( (5, 6) \).
- Therefore, the range of the function (the set of possible \( y \)-values) is from the minimum \( y = -5 \) to the maximum \( y = 9 \).

Thus, the **range** is:
\[
\boxed{[-5, 9]}
\]

### Alternate Set Notation:
In set notation, we can write the range as:
\[
\boxed{\{y \mid -5 \leq y \leq 9\}}
\]

Would you like more details, or do you have any specific questions?

Here are five questions you might consider next:
1. What is the domain of the function?
2. Can you identify the x-intercepts from the graph?
3. How can we classify the function based on its behavior (e.g., polynomial, exponential)?
4. What are the critical points (maxima, minima) of the function?
5. How would you determine if the function is even, odd, or neither?

**Tip:** Always observe both the highest and lowest points on the graph carefully to determine the range.

Determine the range of the following graph and put it in alternate notation.

Learn how to determine the range of a function from a graph. This problem includes a detailed analysis of minimum and maximum y-values, providing the range in interval and set notation. Suitable for high school students.

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