# rational function, polynomial function or some other function

• Sep 14th 2010, 07:55 AM
happy8588
rational function, polynomial function or some other function
Determine if these functions are rational function, polynomial function or some other function and why.

1.) f(x)=2x^-3+5x^-2+6
2.) f(t)=2t^2+t^1/3
3.) f(r)=Gr/(r^3-8)

Thanks
• Sep 14th 2010, 01:40 PM
emakarov
The sum, product, and ratio of rational functions are again rational functions, as are constants and x. Therefore, 1) is a rational function.

In 2), do you mean f(t)? Note that the cubic root is not a rational function.

I am not sure how to parse 3): is it (Gr / (r^3)) - 8? Then why not (G / r^2) - 8? Or is it Gr / (r^3 - 8)? Also, I guess it should be f(r). In any case, the same reasoning as in 1) applies.
• Sep 14th 2010, 02:13 PM
happy8588
in 2.) I do you mean f(t) I typed the wrong variable in.
3..) f(r)=Gr / (r^3 - 8) However how is it a rational number. if i put r as 2 it would not be valid.
• Sep 14th 2010, 02:46 PM
emakarov
Quote:

3..) f(r)=Gr / (r^3 - 8) However how is it a rational number. if i put r as 2 it would not be valid.
If parentheses are like this, then the question why Gr / r^3 is not simplified to G / r^2 does not arise. This is not a rational number, but a rational function because it is a ratio of two rational functions, in fact, of two polynomials. (I assume that Gr is the product of a constant G and r.)