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The function f(x) = x^2 + 3 is continuous for which of the following intervals?

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Question: The function f(x) = x^2 + 3 is continuous for which of the following intervals? (2023)

Options:

  1. (-∞, ∞)
  2. (0, 1)
  3. (1, 2)
  4. (2, 3)

Correct Answer: (-∞, ∞)

Exam Year: 2023

Solution: 

f(x) = x^2 + 3 is a polynomial function and is continuous for all x in (-∞, ∞).

The function f(x) = x^2 + 3 is continuous for which of the following intervals?

Practice Questions

Q1
The function f(x) = x^2 + 3 is continuous for which of the following intervals? (2023)
  1. (-∞, ∞)
  2. (0, 1)
  3. (1, 2)
  4. (2, 3)

Questions & Step-by-Step Solutions

The function f(x) = x^2 + 3 is continuous for which of the following intervals? (2023)
  • Step 1: Identify the function given in the question, which is f(x) = x^2 + 3.
  • Step 2: Recognize that f(x) is a polynomial function because it is made up of x raised to a power (x^2) and a constant (3).
  • Step 3: Understand that polynomial functions are continuous everywhere on the real number line.
  • Step 4: Conclude that since f(x) is a polynomial function, it is continuous for all values of x, which means it is continuous on the interval (-∞, ∞).
  • Continuity of Functions – Understanding that polynomial functions are continuous everywhere on the real number line.
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