To determine the range of the function f(x) = 3x + 12 for the domain x ∈ [-2, 2], we first need to evaluate the function at the endpoints of the given domain.
1. **Evaluate at the lower endpoint:**
– When x = -2:
f(-2) = 3(-2) + 12 = -6 + 12 = 6
2. **Evaluate at the upper endpoint:**
– When x = 2:
f(2) = 3(2) + 12 = 6 + 12 = 18
Now, we can see how the function behaves between these two points. Since f(x) = 3x + 12 is a linear function, it is continuous and increasing over the entire domain. Therefore, the minimum value occurs at the left endpoint, and the maximum value occurs at the right endpoint.
Taking both evaluations into account, the range of f(x) over the domain x ∈ [-2, 2] is:
- Minimum: 6
- Maximum: 18
Thus, the range of the function is:
Range: [6, 18]
This means that for values of x within the interval [-2, 2], the function f(x) will output values ranging from 6 to 18, inclusive.