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Question

Find the range of the function with the given domain.

f(x)=4x−2
𝑓
(
𝑥
)
=
4
𝑥
−
2


Domain: {-2, -1, 0, 1, 2}

What is the range? Choose the correct answer below.

(1 point)
Responses

{6, 2, 2, 6, 10}
{6, 2, 2, 6, 10}

{-10, -6, -2, 2, 6}
{-10, -6, -2, 2, 6}

{-10, -6, -2, -2, 6}
{-10, -6, -2, -2, 6}

{-2, -1, 0, 1, 2}

1 answer

To find the range of the function \( f(x) = 4x - 2 \) with the given domain \({-2, -1, 0, 1, 2}\), we need to calculate \( f(x) \) for each value in the domain:

  1. For \( x = -2 \): \[ f(-2) = 4(-2) - 2 = -8 - 2 = -10 \]

  2. For \( x = -1 \): \[ f(-1) = 4(-1) - 2 = -4 - 2 = -6 \]

  3. For \( x = 0 \): \[ f(0) = 4(0) - 2 = 0 - 2 = -2 \]

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

  5. For \( x = 2 \): \[ f(2) = 4(2) - 2 = 8 - 2 = 6 \]

Now we can collect all the results:

  • \( f(-2) = -10 \)
  • \( f(-1) = -6 \)
  • \( f(0) = -2 \)
  • \( f(1) = 2 \)
  • \( f(2) = 6 \)

The range of the function is the set of all outputs from these calculations: \[ \text{Range} = {-10, -6, -2, 2, 6} \]

Now, let's match this with the given response options. The correct range is: \[ {-10, -6, -2, 2, 6} \]

Thus, the correct answer is: {-10, -6, -2, 2, 6}