Option d: reflect across the y-axis, stretch the graph vertically by a factor of 3, shift 2 units up.
Step-by-step explanation:
The parent function is [tex]f(x)=2^{x}[/tex]
The transformation function is [tex]g(x)=3(2)^{-x} +2[/tex]
In the transformed function, the function is added +2, which shifts the graph by 2 units up.
Also, the function is multiplied by 3, which stretches the function [tex]f(x)=2^{x}[/tex] vertically by a factor of 3 units.
The variable x is multiplied by -1, such that the function reflects across y-axis.
Thus, the correct answer is option d.
The graph is attached below which shows the parent function and the transformed function.
The transformation function is reflect across the y-axis, stretch the graph vertically by a factor of 3, shift 2 units up.
