# How do you sketch the general shape of #f(x)=x^3-2x^2+1# using end behavior?

##### 1 Answer

#### Explanation:

You need to know that the end behaviour of a polynomial depends on its degree:

- if the degree is even, both limits at
#\pm\infty# will be#+\infty# - if the degree is odd, you'll have the limit according to the direction: if
#p(x)# is your polynomial, then#lim_{x\to-\infty}p(x)=-\infty# and#lim_{x\to+\infty}p(x)=+\infty#

This is easy to explain: an even degree means that you surely are the square of something:

On the other hand, you can see an odd power as an even power of

We already observed that

The reason for which the leading term is the only relevant one is simple, too: let's analyze your case: we have

So, if we factor the greatest power of