A technical analyst at 'Apex Manufacturing' is comparing two performance models for a production line: $f(x) = 3x^2 - 5x + 7$ and $g(x) = x^2 - 4x - 3$. To find the net performance difference $(f-g)(x)$, the analyst subtracts the second model from the first. Arrange the following steps in the correct order to reflect the standard procedure for subtracting these specific polynomials.

As a budget analyst at a manufacturing company, you model the weekly revenue with the function $f(x) = 3x^2 - 5x + 7$ and the weekly production costs with $g(x) = x^2 - 4x - 3$. To determine the projected weekly profit, you must calculate the difference between revenue and costs, defined as $(f-g)(x)$. Recalling the specific steps for subtracting these two polynomials, which of the following represents the simplified expression for the weekly profit?

A warehouse manager is comparing two capacity models: $f(x) = 3x^2 - 5x + 7$ and $g(x) = x^2 - 4x - 3$. To determine the available space using $(f-g)(x)$, the manager subtracts the second function from the first. During the simplification process, distributing the negative sign changes the $-4x$ term in $g(x)$ to $+4x$.

Calculating Net Inventory Change

An inventory manager at a logistics center uses the function $f(x) = 3x^2 - 5x + 7$ to model total storage capacity and $g(x) = x^2 - 4x - 3$ to model currently occupied space. To find the available surplus, the manager calculates the difference $(f-g)(x)$. Based on the simplified result of ${}2x^2 - x + 10$ described in your lesson, match each part of the polynomial with its correct numerical value.

A freelance graphic designer models their total monthly service revenue (in dollars) with the function $f(x) = 3x^2 - 5x + 7$ and their monthly software and licensing expenses with $g(x) = x^2 - 4x - 3$, where $x$ represents the number of active client projects. To determine their net monthly earnings, they calculate the difference function $(f-g)(x) = f(x) - g(x)$. When performing this subtraction and fully simplifying the resulting expression, the constant term of the new polynomial is ____.

Documenting Profit Modeling Procedures