The function f(x) = 3x + 12 is a linear function, and we want to find its range when the input x is restricted to the domain of [-2, 2].
To start, we evaluate the function at the endpoints of the domain:
- For x = -2: f(-2) = 3(-2) + 12 = -6 + 12 = 6
- For x = 2: f(2) = 3(2) + 12 = 6 + 12 = 18
Since the function is linear and has a positive slope (3), it will only increase as x moves from -2 to 2. Therefore, the minimum value of the function on this interval occurs at x = -2 (which gives us 6) and the maximum value occurs at x = 2 (which gives us 18).
Thus, the range of the function f(x) when the domain is restricted to [-2, 2] is from 6 to 18, inclusive. We can express the range as:
Range: [6, 18]