1. The problem asks to identify the type of function between options a) polynomial function and b) rational function. 2. Definitions: - A polynomial function is a function of the form $f(x) = a_nx^n + a_{n-1}x^{n-1} + \cdots + a_1x + a_0$ where the exponents are non-negative integers and coefficients are real numbers. - A rational function is a ratio of two polynomials, $f(x) = \frac{P(x)}{Q(x)}$ where $Q(x) \neq 0$. 3. To distinguish between the two: - If the function is expressed as a single polynomial expression with no division by a variable expression, it is a polynomial function. - If the function is expressed as a fraction where numerator and denominator are polynomials, it is a rational function. 4. Therefore, the answer depends on the form of the function given: - If it is a polynomial expression, the answer is a) polynomial function. - If it is a ratio of polynomials, the answer is b) rational function. Since the question asks "between a to b," the answer is that a polynomial function is a special case of a rational function where the denominator is 1. Final answer: The polynomial function (a) is a specific type of rational function (b) where the denominator is 1.