Find the range of the function for the given domain.

Question

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: \[ {1, 4, 7, 10, 13} \]