An operations analyst uses the linear function $g(x) = 3x - 5$ to estimate the total production time (in hours) for $x$ batches of a product. If the analyst needs to evaluate the production time for a quantity of batches represented by the expression $h^2$, which of the following is the correct simplified expression for $g(h^2)$?

A retail analyst uses the linear function $g(x) = 3x - 5$ to predict inventory costs based on variable batch sizes. Match each specific evaluation the analyst might perform with its correct simplified algebraic result.

A production analyst uses the linear function $g(x) = 3x - 5$ to estimate the total operating cost for $x$ machine hours. True or False: For this specific function, the cost of an extended run represented by $g(x + 2)$ is equivalent to the sum of the original cost and the cost of a 2-hour run, $g(x) + g(2)$.

Comparing Function Evaluations in Cost Projections

An operations manager is comparing two different cost projections using the function $g(x) = 3x - 5$. They calculate the cost of increasing the batch size by two, denoted as $g(x+2)$, and compare it to the cost of the original batch plus the cost of two standalone units, denoted as $g(x) + g(2)$. They find that the resulting expressions are ${}3x + 1$ and ${}3x - 4$, respectively. This illustrates the mathematical principle that evaluating a function for a sum is not necessarily ____ to the sum

Reviewing Shipping Rate Calculations in Logistics Billing