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?

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.