Chapter Review
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Start by dividing the numerator by the denominator.
Function: g(x)= -26x+7+4
Graph:
Graph of g as a Transformation of the Graph of f(x)= ax: Translation 7 unit left and 4 units up of the graph of f(x)= -26x.
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.
4x/x= 4
Multiply term by divisor
Subtract down
The quotient is 4 with a remainder of -26. We can rewrite the function using this information. g(x)=4x+2/x+7 ⇔ g(x)=-26/x+7+ 4
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)=-26/x+7+4 ⇔ g(x)=-26/x-( - 7)+ 4 We can see that a= -26, h= - 7, and k= 4. Therefore, the graph of g is a translation 7 unit left and 4 units up of the graph of f(x)= -26x. We will use this information to draw the graph.
