Classify the given function as a polynomial function, rational function, or root function, $$ h(x)=\frac{2}{x^{2}+36} $$

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The function $$ h(x)=\frac{2}{x^{2}+36} $$ is a rational function. The given function is $$ h(x) = \frac{2}{x^{2} + 36}. $$ To classify this function, we can analyze its form: 1. **Polynomial Function**: A polynomial function is a function that can be expressed in the form $$ a_n x^n + a_{n-1} x^{n-1} + \ldots + a_1 x + a_0 $$, where $$ a_n, a_{n-1}, \ldots, a_0 $$ are constants and $$ n $$ is a non-negative integer. The function $$ h(x) $$ does not fit this form because it is not a sum of terms with non-negative integer powers of $$ x $$. 2. **Rational Function**: A rational function is a function that can be expressed as the ratio of two polynomials, i.e., $$ \frac{P(x)}{Q(x)} $$, where $$ P(x) $$ and $$ Q(x) $$ are polynomials. In this case, the numerator is the constant $$ 2 $$ (which can be considered a polynomial of degree 0), and the denominator $$ x^2 + 36 $$ is a polynomial of degree 2. Therefore, $$ h(x) $$ is a rational function. 3. **Root Function**: A root function typically involves expressions like $$ \sqrt{x} $$ or $$ \sqrt[n]{x} $$. The function $$ h(x) $$ does not involve any root expressions. Based on this analysis, we can classify the function $$ h(x) $$ as a **rational function**.

Classify the given function as a polynomial function, rational function, or root function, \( h(x)=\frac{2}{x^{2}+36} \)

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Classify the given function as a polynomial function, rational function, or root function, \( h(x)=\frac{2}{x^{2}+36} \)

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