# How do you describe the end behavior of #f(x)=x^3-4x^2+7#?

##### 1 Answer

Increasingly negative to the left and increasingly positive to the right.

#### Explanation:

In order to determine end behavior, only the highest degree term (term with the highest exponent) matters. Because

We then look for two key factors in determining the end behavior:

**1. Power of the exponent:**

If the power is even (

If the power is odd (

But how do we know if the ends are positive or negative? We have to check the...

**2. Sign of the coefficient:**

If the coefficient is positive, then

- If the highest power is even then both ends go up (think of the graph
#x^2# ; all end behavior for functions with an even highest power will look like that). - If the highest power is odd, then when
#x# is very negative, then#y# will also become very negative and when#x# is very positive,#y# becomes very positive (think#x^3# ).

If the coefficient is negative, then reverse what is above: if the highest power is even, both ends go down and if the highest power is odd, the left goes up and the right goes down.

For your function, since