## Baldwin777 2 years ago f(x)=5+7x^2 Does the f(x) represent a polynomial function?

1. ParthKohli

What do you think?

2. Baldwin777

Yes

3. ParthKohli

How so?

4. Baldwin777

because of the equation

5. ParthKohli

I mean, why do you think it is a polynomial function?

6. Baldwin777

because of the terms? I really honestly don't know if it is

7. Baldwin777

If it is a polynomial function what is it's type?

8. ParthKohli

Well, does it look like this thing?\[ax^2 + bx + c\]If it does, then it's a polynomial function. Remember that \(a,b,c\) can hold the value \(0\) too.

9. Baldwin777

It somewhat looks like that, except that it's flipped

10. ParthKohli

Yeah, but it still is. So it's a polynomial :-)

11. Baldwin777

Okay so what wold the polynomials type be? linear, cubic, quadratic?

12. Aeronautix

A polynomial function is defined as a function f(x) = ax^n + bx^(n-1) + ... + cx^(n-(n-2)) + dx^(n-(n-1)) + ex^(n-n) = ax^n + bx^(n-1) + ... +cx^2 + dx + e. In your equation, c=7 and e=5 are coefficients, and the rest of the coefficients are equal to zero so those terms don't appear. Therefore your f(x) represents a polynomial function.

13. ParthKohli

What is the highest power of \(x\) which you see?

14. ParthKohli

If the highest power is 1, then linear. If 2, then quadratic. If 3, then cubic. If 4, then quartic.

do you mean poly?

16. Baldwin777

Oh, thank you all you really made me understand this a lot better

17. Aeronautix

If it fits the definition of a polynomial function, then it can be called a polynomial function. Math is mostly a lot of definitions! :)