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

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

Options:

  1. 0, Continuous
  2. 0, Discontinuous
  3. 4, Continuous
  4. 4, Discontinuous

Correct Answer: 4, Continuous

Solution: 

f(-1) = (-1)^2 + 3(-1) + 2 = 0. Since f(x) is a polynomial, it is continuous everywhere.

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

Practice Questions

Q1
If f(x) = x^2 + 3x + 2, what is the value of f(-1) and is it continuous?
  1. 0, Continuous
  2. 0, Discontinuous
  3. 4, Continuous
  4. 4, Discontinuous

Questions & Step-by-Step Solutions

If f(x) = x^2 + 3x + 2, what is the value of f(-1) and is it continuous?
  • Step 1: Identify the function f(x) = x^2 + 3x + 2.
  • Step 2: Substitute -1 into the function: f(-1) = (-1)^2 + 3(-1) + 2.
  • Step 3: Calculate (-1)^2, which is 1.
  • Step 4: Calculate 3(-1), which is -3.
  • Step 5: Now combine the results: f(-1) = 1 - 3 + 2.
  • Step 6: Simplify the expression: 1 - 3 = -2, then -2 + 2 = 0.
  • Step 7: Therefore, f(-1) = 0.
  • Step 8: Determine if the function is continuous. Since f(x) is a polynomial, it is continuous everywhere.
  • Function Evaluation – The process of substituting a specific value into a function to find its output.
  • Continuity of Functions – Understanding that polynomial functions are continuous everywhere on their domain.
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