A small business owner uses the function $f(x) = 3^x$ to model the projected growth of a digital subscription service over $x$ months. To account for a fixed monthly operating loss of 2 units, the owner adjusts the model to $g(x) = 3^x - 2$. Based on the rules of vertical translation, how is the graph of $g(x)$ positioned relative to the graph of $f(x)$?

A business analyst uses the base growth model $f(x) = 3^x$ to project revenue. To account for a fixed monthly operational cost, the analyst adjusts the model to $g(x) = 3^x - 2$. True or False: In a coordinate system, the graph of the adjusted model $g(x)$ is positioned exactly 2 units vertically below the graph of the original model $f(x)$.

Vertical Shifts in Exponential Growth Models

A business analyst is using exponential functions to model company growth. Match each mathematical expression or coordinate with its correct description based on the relationship between the functions $f(x) = 3^x$ and $g(x) = 3^x - 2$.

Projecting Net Growth with Operational Overhead

A financial analyst plots two revenue models on the same coordinate system. The gross revenue is modeled by the function $f(x) = 3^x$, and the net revenue, which accounts for fixed overhead costs, is modeled by $g(x) = 3^x - 2$. Based on the rules of graph transformations, the graph of the net revenue model $g(x)$ is exactly the same shape as the graph of $f(x)$ but is shifted vertically ____ by two units.