Final answer:
g(x) = f(-x) represents a horizontal reflection of the function f(x) = 2x + 1 across the y-axis, converting it into g(x) = -2x + 1.
Step-by-step explanation:
The transformation described by the student involves a function f(x) and a transformation g(x) where g(x) is defined as f(-x). In this case, f(x) = 2x + 1, and thus g(x) = f(-x) = 2(-x) + 1 = -2x + 1. This transformation is a reflection of the original function across the y-axis. If we consider the general concept that y(x) = -y(-x) indicates an odd function, which is anti-symmetric with respect to the origin, then the function f(x) = 2x + 1 does not satisfy this condition as it is not symmetric about the origin or the y-axis.
However, by defining g(x) = f(-x), we have applied a transformation that reflects the graph of f(x) across the y-axis. Essentially, the transformation from f(x) to g(x) represents a horizontal reflection. The understanding of transformations is essential in algebra and allows us to predict how the graph of a function will change in response to alterations of its formula.