: Classifying Standard Function Families
(i) Define the following real-valued functions and write their usual algebraic form:
(a) a polynomial function
(b) a rational function
(c) a modulus function
(ii) For each rule given below, state the family (polynomial, rational, modulus or ‘none of these’). Give one brief reason for every answer.
(a) f(x)=5x3−7x+1
(b) g(x)=x−42x+3
(c) h(x)=∣2x−5∣
(d) k(x)=9−x
(iii) For every rule identified as a polynomial in part (ii), state its degree. For every rule identified as rational, name the numerator and denominator polynomials.