Which of the following functions is continuous at all points?

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Question: Which of the following functions is continuous at all points?

Options:

Correct Answer: f(x) = x^3

Solution:

f(x) = x^3 is a polynomial function, which is continuous everywhere.

Which of the following functions is continuous at all points?

Which of the following functions is continuous at all points?

Step 1: Understand what a continuous function is. A function is continuous at a point if you can draw it without lifting your pencil.
Step 2: Identify the type of function given in the question. Here, we have f(x) = x^3.
Step 3: Recognize that x^3 is a polynomial function. Polynomial functions are made up of terms like x raised to whole number powers.
Step 4: Learn that polynomial functions are continuous everywhere on the real number line. This means they do not have any breaks, jumps, or holes.
Step 5: Conclude that since f(x) = x^3 is a polynomial function, it is continuous at all points.

No concepts available.