To determine whether the function in the graph is continuous, let's analyze the graph step by step:

Step-by-Step Analysis:

1. Identify Open and Closed Circles:

   • There is an open circle at $x = -1$, indicating the function is not defined at that point on the main curve.
   • There is also a closed circle (filled in) at $x = -1$, which suggests that the function is defined at $x = -1$, but with a different value from the one in the main curve.

2. Behavior at $x = -1$:

   • Since there is a mismatch between the open circle (on the main curve) and the closed circle (indicating the defined value), this creates a jump discontinuity. The function "jumps" from the value represented by the open circle to the value represented by the closed circle.

3. Overall Continuity:

   • The rest of the graph seems to be continuous as there are no other breaks, jumps, or open circles observed.

Conclusion:

The function is not continuous because there is a jump discontinuity at $x = -1$. The function value changes abruptly from the point on the curve (where the open circle is) to the value represented by the closed circle.

Would you like more details on this topic, or do you have any further questions?

Here are five related questions you might find interesting:

1. What is the difference between a jump discontinuity and a removable discontinuity?
2. How can you formally prove the existence of a discontinuity at a point?
3. What is the significance of limits in determining the continuity of a function?
4. Can a function with a jump discontinuity be differentiable?
5. How would you determine the left-hand and right-hand limits for this function at $x = -1$?

Tip: Always carefully observe the points where the graph has open and closed circles. Open circles generally indicate where a function isn't defined, which helps in identifying discontinuities.