Sketching graph of y =(x^3-2x^2-10x-1)/(x^2-2x-15)

Quote:

Originally Posted by Joker37

Sketch the graph of the following.

$y = \dfrac{x^3-2x^2-10x-1}{x^2-2x-15}$

Any help would be appreciated!

You can write it like those too to help you:

$y = \dfrac{x^3-2x^2-10x-1}{(x-5)(x+3)} = x + \dfrac{3}{x-5} + \dfrac{2}{x+3}$

You know that there are two vertical asymptotes at x = 5 and x = -3, then the graph also tends to the line y = x as x becomes large.

Since there are two asymptotes, the graph is in three parts and as similar graphs, the central part is fairly similar to the numerator, that is a cubic.

Now what you can do is try out what is the value of y slightly to the left and slightly to the right of the asymptotes to know the shape of the graph, whether it's ascending or descending.