The transformation of f(x) on a coordinate plane relative to g(x) is that the graph of g(x) has been shifted three units to the right and two units upward.
[tex]If \ c \ is \ a \ positive \ real \ number. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=g(x) \ are \ represented \ as \ follows:\\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ f(x)=g(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ f(x)=g(x)-c \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{right}: \\ f(x)=g(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{left}: \\ f(x)=g(x+c)[/tex]
By knowing this, we can see that the function [tex]f(x)[/tex] takes the following form:
[tex]f(x)=g(x-c)+k[/tex]
Therefore, we can say that [tex]g(x-3)[/tex] represents shifting the graph three units to the right and ultimately [tex]g(x-3)+2[/tex] tells us that the graph is shifted two units upward. Finally:
