CPM Homework Help : PC Problem 5-64

Without using a calculator, sketch the graph of $f ( x ) = \frac { 7 - 3 x } { x - 2 }$ . First, rewrite $f\left(x\right)$ as a transformation of $y = \frac { 1 } { x }$ .

Computer without a calculator.

Step 1:

Split the $7$ into a $6$ and a $1$ in order to manipulate a Giant One!

Step 2:

Factor.

Step 3:

Simplify.

Step 4:

Now find the any vertical and horizontal asymptotes. Sketch the curve.

$f(x)=\frac{1}{x-2}-\frac{3x-6}{x-2}$

$f(x)=\frac{1}{x-2}-\frac{3(x-2)}{x-2}$

Answer:

$f(x)=\frac{1}{x-2}-3$