Question

Find the range of the function for the given domain.

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

Choose the correct answer below.

(1 point)
Responses

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

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

{1,5,7,11,13}
{
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 evaluate the function at each of the domain values.

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:
\[
f(-2) = 1, \quad f(-1) = 4, \quad f(0) = 7, \quad f(1) = 10, \quad f(2) = 13
\]

The range of the function for the given domain is:
\[
\{1, 4, 7, 10, 13\}
\]

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