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If f(x) = 3x + 2, what is the value of f(1) and is it continuous?

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Question: If f(x) = 3x + 2, what is the value of f(1) and is it continuous?

Options:

  1. 5, Continuous
  2. 5, Not Continuous
  3. 3, Continuous
  4. 3, Not Continuous

Correct Answer: 5, Continuous

Solution: 

f(1) = 3(1) + 2 = 5. Since f(x) is a linear function, it is continuous everywhere.

If f(x) = 3x + 2, what is the value of f(1) and is it continuous?

Practice Questions

Q1
If f(x) = 3x + 2, what is the value of f(1) and is it continuous?
  1. 5, Continuous
  2. 5, Not Continuous
  3. 3, Continuous
  4. 3, Not Continuous

Questions & Step-by-Step Solutions

If f(x) = 3x + 2, what is the value of f(1) and is it continuous?
  • Step 1: Identify the function given, which is f(x) = 3x + 2.
  • Step 2: To find f(1), substitute 1 for x in the function: f(1) = 3(1) + 2.
  • Step 3: Calculate 3(1), which equals 3.
  • Step 4: Add 2 to the result from Step 3: 3 + 2 = 5.
  • Step 5: Therefore, f(1) = 5.
  • Step 6: To check if the function is continuous, note that f(x) is a linear function.
  • Step 7: Linear functions are continuous everywhere, meaning there are no breaks or gaps.
  • Function Evaluation – The process of finding the output of a function for a given input.
  • Continuity of Functions – Understanding that linear functions are continuous everywhere on their domain.
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