We have found an equivalent expression for g.
g(x)=4x-6/x ⇔ g(x)=- 6/x+4
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)=- 6/x+4 ⇔ g(x)=- 6/x- 0+ 4
We can see that a= - 6, h= 0, and k= 4. Therefore, the graph of g is a translation 4 units up of the graph of f(x)= - 6x. We will use this information to draw the graph.
