# How do you graph #(x^2+3x-4)/x#?

##### 1 Answer

Graph

#### Explanation:

A relatively easy approach is to

(1) notice that the function is not defined at

(2) at every other point in its domain the numerator can be divided by denominator getting

(3) graph the latter as a sum of two graphs

Graph of

graph{x+3 [-10, 10, -5, 5]}

Graph of

graph{-4/x [-10, 10, -5, 5]}

Summing these together, we see that around

Outside of the vicinity of point

All we have to find to position the graph more precisely is to find where it crosses the X-axis, that is where the function equals to zero.

This can be accomplished by solving a quadratic equation

Solutions are

That leads us to describe the behavior of the original function as follows.

As

As

After crossing the X-axis at point

At

As

Then the growth gradually becomes more linear and eventually follows approximately the straight line

The final graph looks like this

graph{x+3-4/x [-20, 20, -25, 25]}