The most likely transformation of the original function y = 2^x represented by the graph, considering positive values for both a and b, is option 3, y = b · 2^{ax}.
Step-by-step explanation:
The question is about identifying the correct transformed equation of the original function y = 2^x. To determine how the graph has been transformed, we need to look at the effects of a and b in the functions. For option 3 (y = b · 2^{ax}), multiplying the original function by 'b' would vertically stretch or compress the graph, and raising 2 to the power of 'ax' would horizontally stretch or compress the graph if 'a' is not equal to 1. This transformation is in line with exponential functions, where 'a' and 'b' serve as scaling factors.
The probable question can be: Assuming positive values for both variables \(a\) and \(b\), which equation accurately represents the transformed graph depicted below as an alteration of the original function \(y = 2^x\)?
1. \(y = a \cdot 2^{bx}\)
2. \(y = 2^{ax} + b\)
3. \(y = b \cdot 2^{ax}\)
4. \(y = 2^{x + a} + b\)
5. \(y = a \cdot 2^{x + b}\)