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The question is asking for values of \(a\) where the function \(g(x)\) approaches a different value from the right side than it does from the left side. This means we are looking for points of discontinuity where the left-hand limit and right-hand limit are not equal (i.e., a jump discontinuity).

From the graph:

- At \( x = -3 \), the graph seems continuous. The left-hand and right-hand limits both approach the same value.
- At \( x = -2 \), the left-hand limit goes to negative infinity, and the right-hand limit goes to positive infinity. Therefore, there's a discontinuity.
- At \( x = -1 \), both the left-hand and right-hand limits approach the same value.
- At \( x = 0 \), both limits approach the same value.
- At \( x = 1 \), there is a jump discontinuity. The left-hand limit approaches a negative value, and the right-hand limit approaches a positive value.
- At \( x = 3 \), the function is continuous.

Thus, the values of \(a\) where \( g(x) \) approaches different values from the left and right sides are:

- \( a = -2 \)
- \( a = 1 \)

### Do you want further details or have any other questions?

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Here are 5 related questions to expand your understanding:

1. What are the different types of discontinuities in a function?
2. How can we determine limits graphically at a given point?
3. What is the difference between a jump discontinuity and an infinite discontinuity?
4. How do we evaluate one-sided limits algebraically?
5. What is the significance of continuous functions in real-world applications?

### Tip:
When identifying discontinuities, always check the left-hand limit and right-hand limit to confirm if they are equal or not.

For which value(s) of a does g(x) approach a different number from the right side than it approaches from the left side?

This problem explores the concept of limits and discontinuities. Learn how to identify points where g(x) approaches different values from the left and right sides. We focus on detecting jump discontinuities using graphical analysis, suitable for students in Grades 10-12.

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