continuous function help

[slgardner]

I am having a homework problem! The question is this:
part A--find a continuous function f(x) such that f(-1)=f(2)=f(5)=0 and f(x) not= 0 for all other values of x.

Part b--find a function that is not continuous at x=0, but is continuous for all x not=0.

For part b, I am thinking that (x-1)/x satisfies this but I am not sure at all. Also, I just need some help in the right direction for part A. I do not know where to start on it. Otherwise I generally understand all of the concepts for continuous functions.
Thanks for your ASAP help!
Laura

 

[stapel]

a) Since you need a function that has zeroes at x = -1, x = 2, and x = 5, but no other x-values, then why not use a polynomial with suitable factors?

b) I agree: a function that has one vertical asymptote at x = 0 should do the job. Note: Any such function would do the job! For instance, (x² + 1)/x, |x|/x, or ln(|x|) would also work.

Hope that helps a bit.

Eliz.