Final Answer:
The function g(x) is obtained from f(x)=2ˣ through a vertical stretch by a factor of 3 and a horizontal translation to the right by 2 units.
Step-by-step explanation:
The transformation from f(x)=2ˣ to g(x) involves two main changes: a vertical stretch and a horizontal translation. Firstly, the coefficient 3 in front of 2ˣ indicates a vertical stretch by a factor of 3. This means that each y-coordinate of the points on the graph of f(x) is multiplied by 3, causing the function to stretch vertically.
Secondly, the expression g(x) = f(x - 2) suggests a horizontal translation to the right by 2 units. This means that each x-coordinate of the points on the graph is shifted to the right by 2 units. The minus sign inside the parentheses implies a shift to the right, and the numerical value, 2, represents the magnitude of the translation.
In summary, the transformations applied to f(x)=2ˣ to obtain g(x) are a vertical stretch by a factor of 3 and a horizontal translation to the right by 2 units. These transformations alter the shape and position of the graph, providing a clear understanding of how the original function has been modified.