https://file.aiquickdraw.com/mathbot/file/1725562722206bwixkqro.jpg

The image you uploaded shows a piecewise function with two segments: one represented by a blue line and the other by a green line. 

To determine if the function is continuous, we need to check if the two pieces of the function connect smoothly at the point where they meet. In other words, at the transition point (marked in red), the following conditions must hold for the function to be continuous:
1. The limit of the function from the left side must equal the limit from the right side.
2. The value of the function at the transition point must match these limits.

From the graph:
- The blue line approaches the transition point from the left.
- The green line starts from the transition point and continues to the right.
  
At the transition point, there is a **jump discontinuity**, meaning the two parts do not meet smoothly — the blue line ends below the green line. Therefore, the function is not continuous.

So, the correct answer is **False**.

Would you like any additional explanation or details?

Here are 5 related questions to deepen your understanding:
1. What is the formal definition of a continuous function?
2. What is a piecewise function, and how is it different from a standard function?
3. Can you explain what a jump discontinuity is in mathematical terms?
4. What are the different types of discontinuities?
5. How can you tell if a function is continuous from its equation, rather than its graph?

**Tip:** To determine continuity, always check the behavior of the function at every point where it changes definition or shape.

The piecewise function shown in the graph is a continuous function. True or False?

Analyze the graph of a piecewise function to determine whether it is continuous. This problem covers the concepts of continuity and discontinuity, with a specific focus on jump discontinuities. Suitable for students in Grades 9-12.

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