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Sketching Polynomial Functions

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 has variable terms whose exponents are positive integers and coefficients are real, which means it is a polynomial. Therefore, the function is a polynomial function.

The expression can be rewritten as We see that the exponent is not a positive integer, which means 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 which means the function expression can be written as We see that the exponent is not a positive integer, which means is not a polynomial function.

The third term in the expression has a negative exponent. Thus, it is not a positive integer. The function is not a polynomial function.

The function expression satisfies the conditions of having positive integer exponents and real coefficients, which means is a polynomial function.