A business analyst is using the function $f(x) = 3^x$ to model the organic growth of a company's social media following. To account for a new marketing campaign that adds a fixed baseline of followers, they create a second model: $g(x) = 3^x + 2$. Based on the rules of vertical translation, how is the graph of $g(x)$ positioned relative to the graph of $f(x)$ on a coordinate system?

A social media manager tracks follower growth using the function $f(x) = 3^x$. To account for 2 legacy accounts, they update the model to $g(x) = 3^x + 2$. True or False: The graph of $g(x)$ is a vertical translation that shifts the entire graph of $f(x)$ upward by 2 units.

A growth analyst is comparing two mathematical models for a company's expansion. The base model is $f(x) = {}3^x$, while the second model, $g(x) = {}3^x + 2$, accounts for an additional fixed baseline of 2 units. Match each function or property to its specific graphical feature.

A business analyst is updating a company's revenue growth model. The original model is represented by the function $f(x) = 3^x$. To account for a new guaranteed baseline income of 2 million dollars, the analyst uses the function $g(x) = 3^x + 2$. Arrange the following steps in the correct order to accurately graph the new model $g(x)$ based on the graph of $f(x)$.

Analyzing Vertical Shifts in Growth Models

A business analyst is modeling weekly customer acquisition growth for a retail startup. The base organic growth is modeled by the function $f(x) = 3^x$. To account for a new marketing partnership that guarantees a fixed addition of 2 customers per week, the analyst updates the model to $g(x) = 3^x + 2$. Based on the rules of vertical translation, the horizontal asymptote of the base growth model $f(x)$ is $y = 0$, while the horizontal asymptote of the translated model $g(x)$ is the line $y =$ ____.

Explaining Vertical Translation of Exponential Models