1. The problem asks to identify the type of function for each given case: a) polynomial function, b) rational function, c) square root function, d) other. 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 $$Q(x) \neq 0$$. - A square root function involves the square root of a variable expression, typically $$f(x) = \sqrt{g(x)}$$. - Other functions do not fit into these categories. 3. For each case: - a) Polynomial function: By definition, this is a polynomial function. - b) Rational function: By definition, this is a rational function. - c) Square root function: By definition, this is a square root function. - d) Other: This is any function that does not fit the above categories. Final answer: a) Polynomial function b) Rational function c) Square root function d) Other