### Home > PC3 > Chapter 6 > Lesson 6.2.2 > Problem6-94

6-94.

Graph each rational function. State the equations of the asymptotes.

1. $m(x) =\frac { 3 x - 5 } { x - 4 }$

$m(x)=\frac{3(x-4)+?}{x-4}$

$m(x)=\frac{3(x-4)}{x-4}+\frac{?}{x-4}$

The vertical asymptote occurs when $x − 4 = 0$.
The horizontal asymptote occurs when $x$ is a very large number.
To determine the horizontal asymptote, use the simplified equation from Step 2.
What happens when $x$ is very large?

1. $n(x) =\frac { 4 x ^ { 2 } - 4 } { x ^ { 2 } - 2 }$

Follow the steps outlined in part (a) to rewrite the equation in a friendlier form.

The vertical asymptotes occur when $x^{2} − 2 = 0$.

Hopefully your rewritten equation matches the one shown below.
The determine the horizontal asymptote, think about what value the function approaches when $x$ is a very large number.

$n(x)=4+\frac{4}{x^2-2}$