Question

Find the range of the funtion for the given domain.

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

(1 point)

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 the value of \( f(x) \) for each element 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 can compile the values calculated above to determine the range of \( f \):
- \( f(-2) = 1 \)
- \( f(-1) = 4 \)
- \( f(0) = 7 \)
- \( f(1) = 10 \)
- \( f(2) = 13 \)

Thus, the range of the function \( f(x) \) for the given domain is:
\[
\{1, 4, 7, 10, 13\}
\]