You are a production analyst at a manufacturing facility. The daily production volume of Product A is modeled by the function $f(x) = 3x^2 - 5x + 7$ and the daily production volume of Product B is modeled by $g(x) = x^2 - 4x - 3$, where $x$ represents the number of active assembly lines. Your manager needs to know the combined total daily output when exactly 3 assembly lines are running. Based on the rules for combining functions, which of the following correctly recalls the method to evaluate $(f+g)(3)$ and provides the correct total?

A retail manager uses two functions to model the daily revenue of two different store branches. Branch A is modeled by $f(x) = 3x^2 - 5x + 7$ and Branch B is modeled by $g(x) = x^2 - 4x - 3$, where $x$ represents the number of hours of operation. To determine the financial performance when the branches are open for $x = 3$ hours, match each mathematical component with its correct numerical value or simplified expression.

An operations manager uses the functions $f(x) = 3x^2 - 5x + 7$ to model labor costs and $g(x) = x^2 - 4x - 3$ to model equipment costs, where $x$ represents the number of active loading docks. To find the total combined cost $(f+g)(3)$ by evaluating the functions separately, arrange the following steps in the correct order.

A budget analyst uses the functions $f(x) = 3x^2 - 5x + 7$ to model overhead costs and $g(x) = x^2 - 4x - 3$ to model labor costs for a project, where $x$ represents the number of active workdays. True or False: To find the total combined cost for 3 workdays, denoted as $(f+g)(3)$, the analyst can use the property that $(f+g)(3) = f(3) + g(3)$.

Combined Revenue Analysis

An online seller tracks the daily net financial change (in dollars) of two payment processing accounts:

• Account A's net change is modeled by the function $f(x) = 3x^2 - 5x + 7$
• Account B's net change is modeled by the function $g(x) = x^2 - 4x - 3$ where $x$ represents the number of high-value transactions completed in a single day.

To find the combined daily net change for both accounts when exactly 3 transactions are completed, the seller needs to evaluate the expression $(f+g)(3)$.

The combined daily net change is ____ dollars.

Verifying Automated Cost Calculations