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The function f(x) = 2x + 1 is continuous at which of the following intervals?

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Question: The function f(x) = 2x + 1 is continuous at which of the following intervals?

Options:

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

Correct Answer: (-∞, ∞)

Solution: 

f(x) = 2x + 1 is a linear function and is continuous over the entire real line (-∞, ∞).

The function f(x) = 2x + 1 is continuous at which of the following intervals?

Practice Questions

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

Questions & Step-by-Step Solutions

The function f(x) = 2x + 1 is continuous at which of the following intervals?
  • Step 1: Identify the function given in the question, which is f(x) = 2x + 1.
  • Step 2: Recognize that f(x) = 2x + 1 is a linear function, meaning it forms a straight line when graphed.
  • Step 3: Understand that linear functions are continuous everywhere, meaning there are no breaks, jumps, or holes in the graph.
  • Step 4: Conclude that since f(x) is a linear function, it is continuous over the entire real line, which is represented as (-∞, ∞).
  • Continuity of Functions – Understanding that linear functions are continuous everywhere on the real number line.
  • Linear Functions – Recognizing the properties of linear functions, including their graphs and behavior.
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