# Determine whether the following function is a polynomial function. If the function is a polynomial​ function, state its degree. If it is​ not, tell why not. Write the polynomial in standard form. Then identify the leading term and the constant term. g(x)=3-\frac{x^{2}}{4}

Determine whether the following function is a polynomial function. If the function is a polynomial​ function, state its degree. If it is​ not, tell why not. Write the polynomial in standard form. Then identify the leading term and the constant term.
$g\left(x\right)=3-\frac{{x}^{2}}{4}$
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Step 1
The given function is,
.
From the definition of polynomial function, it can be said that, the given function is a polynomial function.
The highest power of x in the expression $3-\frac{{x}^{2}}{4}$ is 2.
Thus, degree of the polynomial is 2.
Step 2
The standard form of a polynomial function is,

$⇒g\left(x\right)=-\frac{1}{4}{x}^{2}+3$