Which of the following functions is not continuous at x = 1?

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Question: Which of the following functions is not continuous at x = 1?

Options:

Correct Answer: f(x) = { x, x < 1; 2, x >= 1 }

Solution:

The function has a jump discontinuity at x = 1, hence it is not continuous.

Which of the following functions is not continuous at x = 1?

Which of the following functions is not continuous at x = 1?

Step 1: Understand what continuity means. A function is continuous at a point if you can draw it without lifting your pencil.
Step 2: Identify the point we are checking for continuity, which is x = 1.
Step 3: Look at the function's behavior around x = 1. Check if the function has any breaks, jumps, or holes at this point.
Step 4: If the function has a jump (meaning it suddenly changes value) at x = 1, it is not continuous there.
Step 5: Conclude that if there is a jump discontinuity at x = 1, the function is not continuous at that point.

No concepts available.