What is the range of the function f(x) = 12 – 3x for the domain values of -4, -2, 0, 2, and 4?

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To determine the range of the function f(x) = 12 – 3x, we need to evaluate this function for each value in the specified domain: -4, -2, 0, 2, and 4.

Now let’s calculate the function for each domain value:

  • For x = -4:
    • f(-4) = 12 – 3(-4) = 12 + 12 = 24
  • For x = -2:
    • f(-2) = 12 – 3(-2) = 12 + 6 = 18
  • For x = 0:
    • f(0) = 12 – 3(0) = 12
  • For x = 2:
    • f(2) = 12 – 3(2) = 12 – 6 = 6
  • For x = 4:
    • f(4) = 12 – 3(4) = 12 – 12 = 0

Now, let’s gather all the results:

  • f(-4) = 24
  • f(-2) = 18
  • f(0) = 12
  • f(2) = 6
  • f(4) = 0

The calculated output values for the function are 24, 18, 12, 6, and 0. Therefore, the range of the function for the given domain is:

  • Range: {0, 6, 12, 18, 24}

In conclusion, the range of the function f(x) = 12 – 3x for the specified domain is composed of the output values found by evaluating the function, which are 0, 6, 12, 18, and 24.

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