### Home > PC > Chapter 5 > Lesson 5.2.2 > Problem5-64

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 $y = \frac { 1 } { x }$.

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

Factor.

Simplify.

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

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

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

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