The function f(x) = x^3 - 3x is continuous at which of the following points? (20

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Question: The function f(x) = x^3 - 3x 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^3 - 3x is a polynomial function and is continuous at all points, including -2, 0, and 2.

The function f(x) = x^3 - 3x is continuous at which of the following points? (2023)

The function f(x) = x^3 - 3x is continuous at which of the following points? (2023)

Step 1: Understand what a continuous function is. A function is continuous if you can draw it without lifting your pencil from the paper.
Step 2: Identify the type of function given. The function f(x) = x^3 - 3x is a polynomial function.
Step 3: Know that polynomial functions are continuous everywhere. This means they do not have any breaks, holes, or jumps.
Step 4: Since f(x) is a polynomial, it is continuous at all points on the number line, including the specific points -2, 0, and 2.

Continuity of Polynomial Functions – Polynomial functions are continuous everywhere on the real number line.