Question

Find the range of the function for the given domain.

f(x)=3x+7;{−2,−1,0,1,2}

Choose the correct answer below.

(1 point)
Responses

{1,4,7,10,13}
start set 1 comma 4 comma 7 comma 10 comma 13 end set

{0,4,7,10,14}
start set 0 comma 4 comma 7 comma 10 comma 14 end set

{1,5,7,11,13}
start set 1 comma 5 comma 7 comma 11 comma 13 end set

{1,5,6,11,13}

Answer 1

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

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

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 have calculated the function values:
- \(f(-2) = 1\)
- \(f(-1) = 4\)
- \(f(0) = 7\)
- \(f(1) = 10\)
- \(f(2) = 13\)

The range of the function for the given domain is \(\{1, 4, 7, 10, 13\}\).

Thus, the correct answer is:
\[
\{1, 4, 7, 10, 13\}
\]