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{{ printedBook.courseTrack.name }} {{ printedBook.name }} A polynomial function is a function which is a polynomial, which means that the variables' exponents are positive integers and their coefficients are real numbers. Let's examine one function at a time.

We see that the function $x_{5}+5x_{4}−x_{2}−7$ has variable terms whose exponents are positive integers and coefficients are real, which means it is a polynomial. Therefore, the function $p(x)$ is a polynomial function.

The expression $x1 $ can be rewritten as $x_{-1}.$ We see that the exponent is not a positive integer, which means $q(x)$ is **not** a polynomial function.

Here, we rewrite the function expression in order to see if it's a polynomial. A square root is the same thing as raising to the power of $21 ,$ which means the function expression can be written as $x_{1/2}+2.$ We see that the exponent is not a positive integer, which means $f(x)$ is **not** a polynomial function.

The third term in the expression $x_{7}+x_{6}+x_{-5}−1$ has a negative exponent. Thus, it is not a positive integer. The function $g(x)$ is **not** a polynomial function.

The function expression $4x_{2}+x−3$ satisfies the conditions of having positive integer exponents and real coefficients, which means $h(x)$ is a polynomial function.