Final answer:
a)'f of x equals negative 2x plus 17'. The correct way to read the function notation is Neither of the provided options 'y = 13x' or 'y = x²' correctly describe a function with a positive value,
Step-by-step explanation:
The correct answer is option "a) 'f of x equals negative 2x plus 17'". In function notation, this expression means that the function named 'f' takes an input 'x' and transforms it according to the rule '-2x + 17'.
When reading the notation aloud, it emphasizes the relationship between 'f' and 'x', meaning that 'f' depends on 'x'. This contrasts with option 'b,' which could imply multiplication, option 'c,' which suggests division, and option 'd,' which indicates the derivative of the function with respect to 'x'.
When considering the provided function scenario at x = 3, where the function f(x) has a positive value and a positive slope that is decreasing, we must determine which option could correspond to f(x). Given the two options provided, option 'b. y = x²' could represent a function with these characteristics.
The function y = x² is a parabola opening upwards with a vertex at the origin (0,0) and has a slope that increases as x moves away from the vertex, which does not match the decreasing slope described.
Therefore, option 'a. y = 13x' might seem a plausible answer at first because linear functions have a constant slope; however, its slope would not decrease with increasing x, so this contradicts the given conditions.
Given that no correct answer matches the scenario, we would need additional information or options to accurately identify a function that fits the given properties.