In a business logistics model, the function $g(x) = 4x - 7$ is used to calculate the overhead cost for $x$ units of inventory. To accurately update the model for different inventory scenarios, match each functional notation with its correct initial substitution or setup step.

In a company's resource management system, the function $g(x) = 4x - 7$ is used to calculate the daily operating cost based on the number of active workstations ($x$). An analyst needs to determine the difference between the current operating cost $g(x)$ and the baseline cost when only 3 workstations are active, represented by $g(x) - g(3)$. Arrange the following steps in the correct order to simplify this expression according to the process described in the course.

A small business owner uses the linear function $g(x) = 4x - 7$ to calculate the monthly maintenance cost for $x$ pieces of equipment. If the owner needs to evaluate the cost for a scenario with $(x - 3)$ pieces of equipment, which expression represents the simplified form of $g(x - 3)$ as demonstrated in the course example?

A manufacturing supervisor uses the function $g(x) = 4x - 7$ to calculate the hourly output of a production line. To determine the difference in output between a full shift $g(x)$ and a partial shift of 3 hours $g(3)$, the supervisor must first calculate the constant value of $g(3)$. Based on the function provided, $g(3) = \_\_\_\_$.

Evaluating Functions with Binomial Inputs

In an organization's logistics planning department, an analyst uses the function $g(x) = 4x - 7$ to model the weekly fuel cost (in hundreds of dollars) based on $x$ delivery truck routes. When evaluating $g(x-3)$, which models the cost when there are 3 fewer active routes, the analyst's first step is to substitute the binomial $(x-3)$ for $x$. Is it true or false that this initial, unsimplified substitution step is written as $g(x-3) = 4(x-3) - 7$?

Evaluating Operational Cost Models with Variable Inputs