Math eBook: Monotonic Functions - eCourses.ou.edu

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That is if x1 > x2, then f(x1) > f(x2). On the other hand, a function is called decreasing on an interval if the function value decreases as the independent ...       Search     MATHEMATICS-THEORY     Inthissection,theconceptofamonotonicfunctionisdiscussedandthemethodtofindafunction'smonotonicityisintroduced.           Monotonicity IncreasingFunction DecreasingFunction   Inengineeringresearch,sometimesadiagram canhelptheresearcherbetterunderstandafunction.Afunction'sincreasing ordecreasingtendencyisusefulwhensketchingadraft. Afunctioniscalledincreasingonanintervalifthefunction valueincreasesastheindependentvalueincreases.Thatisifx1>x2, thenf(x1)>f(x2).Ontheotherhand,afunction iscalleddecreasingonanintervalifthefunctionvaluedecreasesas theindependentvalueincreases.Thatisifx1>x2, thenf(x1)0.Therefore,functionf(x)=x2- 4isincreasingintherangeof(-∞,0)anddecreasingintherange of(0,+∞).Thisresultisconfirmedbythediagramontheleft.      



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