The function f(x) = x^2 -2x + x^1/2 is:

A. A polynomial because it is continuous.
B. A polynomial because it is of the form axn.
C. Not a polynomial because you are subtracting 2x.
D. Not a polynomial because you can’t have any fractional exponents.

Is the answer D?

@ms sue?

Yes, the answer is D. The function f(x) = x^2 - 2x + x^(1/2) is not a polynomial because it contains a fractional exponent.

To arrive at this conclusion, we need to understand the definition of a polynomial. A polynomial is a mathematical expression with one or more terms, where each term consists of a variable raised to a non-negative integer power, multiplied by a coefficient. In other words, a polynomial has only whole number exponents.

In the given function, f(x) = x^2 - 2x + x^(1/2), the term x^(1/2) contains a fractional exponent (1/2). This violates the requirement for a polynomial, as the exponent should be a non-negative integer.

Hence, the correct answer is D - "Not a polynomial because you can’t have any fractional exponents."