Final answer:
Given a linear function with f(3) = 7 and a slope of 2.5, to find f(4), we add the slope to f(3) and determine that f(4) = 9.5, which is option A.
Step-by-step explanation:
The given linear function is f(x) with f(3) = 7 and a slope of 2.5. To find f(4), we need to use the concept of slope, which tells us how much the function value changes for each unit increase in x. The slope is the 'rise over run', or in this case, how much f(x) increases when x increases by 1.
Since the slope is 2.5, this means that for every increase of 1 in x, f(x) increases by 2.5. To find f(4), which is one unit more than 3, we simply add the slope to the previous value f(3).
f(4) = f(3) + (slope * (4 - 3))
= 7 + (2.5 * 1)
= 7 + 2.5
= 9.5
Therefore, f(4) = 9.5, which corresponds to option A).