Given the function: f(x)=x^3(x-2)^2 , on the interval [-1,3] find the domain and Asymptotes

...Isn't the domain (-1<x<3) ? and as for the asymptotes I thought you could only find them for rational functions and since that function is not rational I guess there aren't any...???

I agree with you, although I don't know whay you say it isn't a rational function. The domain is [-1,3]. It makes no sense to ask for asymptotes in a limited interval. The function never approaches straight-line behavior.

yes that's what I thought. Thank you!

To determine the domain of a function, we need to consider the values of x for which the function is defined. In this case, the function f(x) = x^3(x-2)^2 does not have any restrictions on the values of x. Therefore, the domain of this function is all real numbers.

Regarding asymptotes, you are correct that asymptotes typically appear in rational functions. A rational function is defined as a function that can be expressed as the quotient of two polynomials. However, the given function f(x) = x^3(x-2)^2 is neither a quotient of polynomials nor does it involve any fractions. Therefore, it does not have any horizontal or vertical asymptotes.

In summary, the domain of the function f(x) = x^3(x-2)^2 is (-∞, ∞), and it does not have any asymptotes.