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Concept · Functions & Sequences
Determining the domain
denominator nonzero, even-root radicand ≥0, log argument >0, non-integer-power base >0; intersect conditions
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Key formulas
9- Functiony = f(x), domain D, range Requal functions require same domain AND same rule
- Domain conditionsdenominator ≠ 0even-root radicand ≥ 0log argument > 0base of non-integer power > 0intersect all conditions
- Even: f(−x) = f(x) (symmetric about y-axis)Odd: f(−x) = −f(x) (symmetric about origin)parity requires a domain symmetric about 0
- Power functiony = xa (coefficient must be 1)
- Exponentialy = ax (a>0, a≠1)natural base e
- Logarithmy = loga x, inverse of axln = loge, lg = log10
- Log rulesloga(MN)=loga M+loga Nloga(M/N)=loga M−loga Nloga(Mk)=k·loga M
- Change of baseloga b = logc b / logc aidentities aloga N=N, loga(an)=n
- Periodicityf(x + T) = f(x)
Shaky underneath?
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FoundationsPrecalculus bridgeAlgebra 2 foundations