To find the range of the function f(x) = 4 – 2x over the domain [0, 5], we first need to evaluate the function at the endpoints of the domain.
1. **Calculate f(0):**
Substituting x = 0 into the function:
f(0) = 4 – 2(0) = 4
2. **Calculate f(5):**
Now, substituting x = 5 into the function:
f(5) = 4 – 2(5) = 4 – 10 = -6
3. **Determine the behavior of the function:**
Since the function f(x) = 4 – 2x is a linear function with a negative slope (-2), it is decreasing throughout its domain. This means that as x increases from 0 to 5, the value of f(x) will decrease from f(0) = 4 to f(5) = -6.
4. **Identify the range:**
Thus, the range of f(x) when x is in the interval [0, 5] is from the maximum value of 4 to the minimum value of -6. We can express this as:
Range: [-6, 4]
In conclusion, the range of the function f(x) = 4 – 2x for the domain [0, 5] is [-6, 4].