A technical analyst is modeling a system's output by multiplying two input functions: $f(x) = 3x - 2$ and $g(x) = 5x + 1$. To compute $(f \cdot g)(x)$, the analyst uses the FOIL method to expand the expression $(3x - 2)(5x + 1)$. Match each specific step of the FOIL process with the correct mathematical term it produces in the expansion.

A production manager is modeling total revenue by finding the product of two functions: $f(x) = 3x - 2$ and $g(x) = 5x + 1$. According to the definition of function multiplication, which of the following is the correctly simplified expression for $(f \cdot g)(x)$?

A project manager is estimating total labor costs by multiplying the number of active work crews, $f(x) = 3x - 2$, by the average daily rate per crew, $g(x) = 5x + 1$. Arrange the following steps in the correct order to recall the derivation of the total cost function $(f \cdot g)(x)$.

Recalling the Multiplication of Two Linear Functions

Recalling the Steps of Function Multiplication

An office operations manager uses two linear models to estimate monthly paper supplies: the number of active administrative departments is modeled by $f(x) = 3x - 2$, and the average boxes of paper used per department is modeled by $g(x) = 5x + 1$. To construct the total supply function $(f \cdot g)(x)$, the manager multiplies the two functions: $(f \cdot g)(x) = (3x - 2)(5x + 1)$. After expanding this product to ${}15x^2 + 3x - 10x - 2$ and combining the like terms, the coefficient of the linea