Question

Which of the following is a polynomial function?

• A. $f\left(x\right)=x^{-2}+x-1$
• B. $f\left(x\right)=\frac{1}{x^2}+4x-8$
• C. $f\left(x\right)=a{x}^2+bx+7$, where $a,b\in R$
• D. $f\left(x\right)=\frac{1}{x}-1$

Answer 1

The correct option is C $f\left(x\right)=a{x}^2+bx+7$, where $a,b\in R$

The polynomial function is of the form $f\left(x\right)=a_n{x}^n+a_{n-1}{x}^{n-1}+a_{n-2}{x}^{n-2}+\cdots +a_0$
where $n\in W$ and $a_n\ne 0$

$a_n\ne 0$ because only then we can have a polynomial of degree $n$ otherwise the term containing $x^n$ would be equal to $0$.

Hence clearly only $f\left(x\right)=a{x}^2+bx+7$, where $a,b\in R$
is a polynomial function.