Final answer:
The function g(x) requires more information on f(x) to be fully evaluated. For the provided example, at x = 3 the function option that is positive with a positive, but decreasing slope is y = x². The equation y = 10 + 5x - 3x² is not linear because it contains a quadratic term.
Step-by-step explanation:
The initial question about the function g(x) cannot be answered without more information on f(x). We are only given the value and slope (derivative) of f(x) at a single point, x = -5. Hence, we can only make assertions about f(-5) and f'(-5), not the entirety of f(x). However, based on the given example, let's address the provided sample question.
If we have a function f(x) that has a positive value and a positive, but decreasing slope at x = 3, the likely choice would be b. y = x². This is because the slope (first derivative) of y = x² is 2x, which is positive but decreasing as x increases. Option a, y = 13x, has a constant slope and does not fit the description. To find the equation that expresses the total fee in terms of the number of days the payment is late, we would need additional context or a formula to construct a response. However, the last question about whether the equation y = 10 + 5x - 3x² is linear can be answered as it is not linear because it includes an x² term, making it a quadratic equation.