We have found an equivalent expression for g.
g(x)=2x+3/x ⇔ g(x)=3/x+2
Describing the Graph as a Transformation of f(x)= ax and Graphing
Let's start by recalling two possible transformations of the function f(x)= ax.
Function
Transformation of the Graph of f(x)= ax
g(x)=a/x- h
Horizontal translation by h units. If h>0, the translation is to the right. If h<0, the translation is to the left.
g(x)=a/x+ k
Vertical translation by k units. If k>0, the translation is up. If k<0, the translation is down.
Now consider the obtained equation.
g(x)=3/x+2 ⇔ g(x)=3/x- 0+ 2
We can see that a= 3, h= 0, and k= 2. Therefore, the graph of g is a translation 2 units up of the graph of f(x)= 3x. We will use this information to draw the graph.
