# How do you find the end behavior of #(5x^2-4x+4) / (3x^2+2x-4)#?

##### 2 Answers

See explanation and graph.

#### Explanation:

y-intercept ( x = 0 ) :

Vertical asymptotes:

As

So, horizontal asymptote:

Interestingly, this asymptote cuts the graph in

Yet it is tangent at

There are two turning points at x = 0.1309 ( in

( in

There exists a point of inflexion for an x between 11/3 and 2.1164.

graph{y(3x^2+2x-4)-(5x^2-4x+4)=0 [-20, 20, -10, 10]}

End behaviour describes what the graph is doing at the ends. It answers what the y values are doing as x values approach each of the ends.

#### Explanation:

Looking at the graph in the previous answer, we see there is a horizontal asymptote

For end behavior, there are 6 ends to consider:

1) as

2) as

3) as

4) as

5) as

6) as