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Use the graph of the function to identify the zeros of the function and their possible multiplicities.


From the graph of the function, we observe the following zeros and their corresponding multiplicities:

- The function has a zero at \( x = -3 \), where the graph crosses the x-axis in a linear manner (not touching and turning back), indicating a multiplicity of 1.
- The function has a zero at \( x = -2 \), where the graph crosses the x-axis in a linear fashion as well, implying a multiplicity of 1.
- The function has a zero at \( x = 1 \), where the graph touches the x-axis and then turns around (does not cross it), suggesting that the multiplicity is 3.

Thus, the correct answer is:

**A.** \( -3 \) with multiplicity 1, \( -2 \) with multiplicity 1, and \( 1 \) with multiplicity 3.

Let me know if you'd like further clarification or have any questions! 

Here are some related questions you might find useful:

1. How does the multiplicity of a zero affect the shape of the graph at that zero?
2. How can we find the multiplicities of zeros for higher-degree polynomials?
3. What is the significance of turning points in polynomial graphs?
4. How do you differentiate between even and odd multiplicities on a graph?
5. What is the relationship between the degree of a polynomial and its number of zeros?

Tip: Always look at how the graph behaves near the zero—whether it crosses or merely touches the axis—to determine the multiplicity!

Use the graph of the function to identify the zeros of the function and their possible multiplicities.

Learn how to identify the zeros of a function and determine their multiplicities based on the graph of the function. This problem involves understanding how the graph crosses or touches the x-axis, which is key to determining the multiplicities of the zeros. Suitable for high school students (Grades 9-12).

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