To determine the equation of the transformed function [tex]\( g \)[/tex] in terms of [tex]\( f(x) \)[/tex], we start with the parent function [tex]\( f(x) = e^x \)[/tex].
Given that the transformation involves multiplying the parent function [tex]\( f(x) \)[/tex] by a scalar [tex]\( a \)[/tex], the equation can be expressed as:
[tex]\[ g(x) = a \cdot f(x) \][/tex]
Since [tex]\( f(x) = e^x \)[/tex], we substitute [tex]\( f(x) \)[/tex] into the above equation:
[tex]\[ g(x) = a \cdot e^x \][/tex]
Thus, the equation for the transformed function [tex]\( g \)[/tex] in terms of [tex]\( f(x) \)[/tex] and the scalar [tex]\( a \)[/tex] is:
[tex]\[ g(x) = a \cdot e^x \][/tex]
This equation represents the transformed function, where [tex]\( a \)[/tex] acts as a scaling factor to the original exponential function [tex]\( f(x) = e^x \)[/tex].
