Thread: rational function, polynomial function or some other function

1. 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

2. 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.

3. 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.

4. 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.)