Final answer:
To identify the symbolic representation of the function, the slope was calculated using the given f(x) values. The slope is found to be -40, which leads to the function being f(x) = -40x, making option B the correct answer.
Step-by-step explanation:
To determine the symbolic representation of the given function from the information provided, we need to identify the pattern that links the inputs (x-values) to the outputs (f(x) values). Given that f(3) = -40 and f(4) = -80, we can calculate the rate of change between these two points to find the slope of the function, which is the coefficient of x in the linear function.
The change in the output (f(x)) when x increases from 3 to 4 is:
f(4) - f(3) = (-80) - (-40) = -40
The change in the input (x) is:
4 - 3 = 1
Thus, the slope (m) of the function is:
m = Change in output / Change in input = -40 / 1 = -40
Therefore, the function must be of the form f(x) = -40x, which means that option B is correct.