# What is the domain and range of #f(x)=x^4-4x^3+4x^2+1#?

##### 1 Answer

The domain of

#### Explanation:

Given:

#f(x) = x^4-4x^3+4x^2+1#

I'm not sure what tools I'm really supposed to use under 'Algebra', but the easiest way to find where the turning points of

#f'(x) = 4x^3-12x^2+8x = 4x(x^2-3x+2) = 4x(x-1)(x-2)#

So

Since the coefficient of the highest degree term

We find:

In common with any polynomial, the domain of

The range of

graph{x^4-4x^3+4x^2+1 [-4, 6, -0.82, 4.18]}