(Section 1.1: Functions)1.1.7 WARNING 6:As a matter of convenience, some sources refer to fx()as a function, but this convention is often rejected as non-rigorous. • One advantage to the notation is that it indicates thatfis a function of onevariable. The notation ,yindicates thatfis a function of twovariables. • A function can be determined by a domainand a function rule. Together, the domain and the function rule determine the rangeof the function. (See Footnote 1.) • Two functions with the same rule but different domainsare considered to be different. • Piecewise-defined functionswill be discussed in Section 1.5. Such a function applies different rules to disjoint (non-overlapping) subsets of its domain (subdomains). For example, consider the functionf, where: =x2,±2²x<1x+1,1²x²2³´µ¶PART E: POLYNOMIAL, RATIONAL, AND ALGEBRAIC FUNCTIONSReview Section 0.6 on polynomial, rational, and algebraic
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