Big Ideas Math Algebra 2, 2014
BI
Big Ideas Math Algebra 2, 2014 View details
4. Adding and Subtracting Rational Expressions
Continue to next subchapter

Exercise 9 Page 386

Start by rewriting the given rational function by inspection.

Function: g(x)=2/x-3+2
Graph:

Graph of g as a Transformation of the Graph of f(x)= ax: Translation 3 units right and 2 units up of the graph of f(x)= 2x.

Practice makes perfect

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.

Rewriting the Function

We want to rewrite the given rational function so that it is in the form g(x)= ax-h+k. We will do it by inspection.
g(x)=2x-4/x-3
g(x)=2x -6+2/x-3
g(x)=2x-6/x-3+2/x-3
g(x)=2(x-3)/x-3+2/x-3
g(x)=2(x-3)/x-3+2/x-3
g(x)=2+2/x-3
g(x)=2/x-3+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)=2/x- 3+ 2 We can see that a= 2, h= 3, and k= 2. Therefore, the graph of g is a translation 3 units right and 2 units up of the graph of f(x)= 2x. We will use this information to draw the graph.