# How do you find the end behavior of # f(x) = (x+1)^2(x-1) #?

##### 1 Answer

as

#### Explanation:

The degree of the polynomial is

Since the degree is odd, you know that

Look at the mother functions:

as

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

as

graph{x^2 [-10, 10, -5, 5]}

as

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

as

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

Let's examine a cubic: if we change the sign of the first term, what happens?

as

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

However, in our case, we know that the leading term will be positive, so the graph will start "down" and then go "up".

Its end behavior:

as

We can check on a graph:

graph{(x+1)^2(x-1) [-10, 10, -5, 5]}