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Find the range of the funtion for the given domain.

f(x) = 3x + 7; {-2,-1,0,1,2}

(1 point)
Responses

{1,4,7,10,13}
{1,4,7,10,13}

{0,4,7,10,14}
{0,4,7,10,14}

{1,5,7,11,13}
{1,5,7,11,13}

{1,5,6,11,13}

1 answer

To find the range of the function \( f(x) = 3x + 7 \) for the given domain \( {-2, -1, 0, 1, 2} \), we need to evaluate the function at each value in the domain.

  1. For \( x = -2 \): \[ f(-2) = 3(-2) + 7 = -6 + 7 = 1 \]

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

  3. For \( x = 0 \): \[ f(0) = 3(0) + 7 = 0 + 7 = 7 \]

  4. For \( x = 1 \): \[ f(1) = 3(1) + 7 = 3 + 7 = 10 \]

  5. For \( x = 2 \): \[ f(2) = 3(2) + 7 = 6 + 7 = 13 \]

Now, we compile the outputs from all the evaluations:

  • \( f(-2) = 1 \)
  • \( f(-1) = 4 \)
  • \( f(0) = 7 \)
  • \( f(1) = 10 \)
  • \( f(2) = 13 \)

Thus, the range of the function \( f(x) \) for the given domain is: \[ {1, 4, 7, 10, 13} \]

The correct response is: {1, 4, 7, 10, 13}.