The function f(x) = x^2 is continuous at which of the following points? (2023)

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Question: The function f(x) = x^2 is continuous at which of the following points? (2023)

Options:

Correct Answer: All of the above

Exam Year: 2023

Solution:

The function f(x) = x^2 is a polynomial function and is continuous at all points, including -1, 0, and 1.

The function f(x) = x^2 is continuous at which of the following points? (2023)

The function f(x) = x^2 is continuous at which of the following points? (2023)

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 function given, which is f(x) = x^2.
Step 3: Recognize that f(x) = x^2 is a polynomial function.
Step 4: Know that polynomial functions are continuous everywhere on the real number line.
Step 5: Conclude that since f(x) = x^2 is continuous everywhere, it is also continuous at the specific points -1, 0, and 1.

Continuity of Functions – Understanding that polynomial functions, such as f(x) = x^2, are continuous everywhere on the real number line.