ConceptFunctions & Sequences

Key formulas

Function: y = f(x), domain D, range R; equal functions require same domain AND same rule
Domain conditions: denominator ≠ 0; even-root radicand ≥ 0; log argument > 0; base of non-integer power > 0; intersect 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 function: y = x^a (coefficient must be 1)
Exponential: y = a^x (a>0, a≠1); natural base e
Logarithm: y = log_a x, inverse of a^x; ln = log_e, lg = log₁₀
Log rules: log_a(MN)=log_a M+log_a N; log_a(M/N)=log_a M−log_a N; log_a(M^k)=k·log_a M
Change of base: log_a b = log_c b / log_c a; identities a^{log_a N}=N, log_a(aⁿ)=n
Periodicity: f(x + T) = f(x)

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FoundationsPrecalculus bridge Algebra 2 foundations

Exponential functions a^x

graphs/properties by base, domain/range/asymptote; natural exponential e

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Exponential functions ax

Exponential functions a^x