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15.

Find the range of ƒ(x) = –x + 4 for the domain {–3, –2, –1, 1}.

{7, 6, 5, 3}

{–7, –6, –5, –4}

{7, 6, 5, 4}

{–7, –6, –5, 3}

1 answer

To find the range of the function \( f(x) = -x + 4 \) for the domain \( {-3, -2, -1, 1} \), we will compute \( f(x) \) for each value in the domain.

  1. For \( x = -3 \): \[ f(-3) = -(-3) + 4 = 3 + 4 = 7 \]

  2. For \( x = -2 \): \[ f(-2) = -(-2) + 4 = 2 + 4 = 6 \]

  3. For \( x = -1 \): \[ f(-1) = -(-1) + 4 = 1 + 4 = 5 \]

  4. For \( x = 1 \): \[ f(1) = -(1) + 4 = -1 + 4 = 3 \]

Now, we collect the outputs we have computed from the function:

  • \( f(-3) = 7 \)
  • \( f(-2) = 6 \)
  • \( f(-1) = 5 \)
  • \( f(1) = 3 \)

Thus, the range of \( f(x) \) is: \[ { 7, 6, 5, 3 } \]

So, the correct answer is:

{7, 6, 5, 3}