Question

Find the range of the function for the given domain.

f(x)=2x−4;{−2,−1,0,1,2}

Choose the correct answer below.

(1 point)
Responses

{−8,−6,−4,−2,0}
start set negative 8 comma negative 6 comma negative 4 comma negative 2 comma 0 end set

{−8,−6,−2,0,2}
start set negative 8 comma negative 6 comma negative 2 comma 0 comma 2 end set

{−8,−6, 0, 2, 4}
{−8,−6, 0, 2, 4}

{0,2,4,6,8}

Answer 1

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

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

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

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

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

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

Now, we have calculated the following values for \( f(x) \):
- \( f(-2) = -8 \)
- \( f(-1) = -6 \)
- \( f(0) = -4 \)
- \( f(1) = -2 \)
- \( f(2) = 0 \)

Now, let's summarize the results to find the range of the function \( f(x) \) over the given domain:
- The values obtained are \( \{-8, -6, -4, -2, 0\} \).

Now we can choose the correct response based on the calculated range.
The correct answer is:

\(\{-8, -6, -4, -2, 0\}\)