anonymous
  • anonymous
f(x)=5+7x^2 Does the f(x) represent a polynomial function?
Mathematics
chestercat
  • chestercat
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ParthKohli
  • ParthKohli
What do you think?
anonymous
  • anonymous
Yes
ParthKohli
  • ParthKohli
How so?

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anonymous
  • anonymous
because of the equation
ParthKohli
  • ParthKohli
I mean, why do you think it is a polynomial function?
anonymous
  • anonymous
because of the terms? I really honestly don't know if it is
anonymous
  • anonymous
If it is a polynomial function what is it's type?
ParthKohli
  • 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.
anonymous
  • anonymous
It somewhat looks like that, except that it's flipped
ParthKohli
  • ParthKohli
Yeah, but it still is. So it's a polynomial :-)
anonymous
  • anonymous
Okay so what wold the polynomials type be? linear, cubic, quadratic?
anonymous
  • anonymous
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.
ParthKohli
  • ParthKohli
What is the highest power of \(x\) which you see?
ParthKohli
  • ParthKohli
If the highest power is 1, then linear. If 2, then quadratic. If 3, then cubic. If 4, then quartic.
anonymous
  • anonymous
do you mean poly?
anonymous
  • anonymous
Oh, thank you all you really made me understand this a lot better
anonymous
  • anonymous
If it fits the definition of a polynomial function, then it can be called a polynomial function. Math is mostly a lot of definitions! :)

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