Chapter Review
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Start by dividing the numerator by the denominator.
Function: g(x)= -1x-1+9
Graph:
Graph of g as a Transformation of the Graph of f(x)= ax: Translation 1 unit right and 9 units up of the graph of f(x)= -1x.
We will rewrite the function, describe the graph of g as a transformation of the graph of f(x)= ax, and draw the graph of g.
9x/x= 9
Multiply term by divisor
Subtract down
The quotient is 9 with a remainder of -1. We can rewrite the function using this information. g(x)=9x-10/x-1 ⇔ g(x)=-1/x-1+ 9
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)=-1/x-1+9 ⇔ g(x)=-1/x- 1+ 9 We can see that a= -1, h= 1, and k= 9. Therefore, the graph of g is a translation 1 unit right and 9 units up of the graph of f(x)= -1x. We will use this information to draw the graph.
