Question

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


{7, 6, 5, 4}


{–7, –6, –5, 3}


{7, 6, 5, 3}


{–7, –6, –5, –4}

Answer 1

To find the range of the function \( f(x) = -x + 4 \) for the given domain \( \{ -3, -2, -1, 1 \} \), we will evaluate the function at each point in the domain and collect the results.

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 can gather the output values from the evaluations:

- For \( x = -3 \), \( f(-3) = 7 \)
- For \( x = -2 \), \( f(-2) = 6 \)
- For \( x = -1 \), \( f(-1) = 5 \)
- For \( x = 1 \), \( f(1) = 3 \)

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

Therefore, the correct answer is:

**{7, 6, 5, 3}**.