Summary (Grade 12 NSC Matric Mathematics): Flashcards

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Definition of a function

Rule that gives exactly one output for each input

Vertical line test purpose

Determines if a graph represents a function

What f−1(x)f^{-1}(x) does

Undoes what the original function does

Reflection line for function and its inverse

y=xy = x

Domain and range swap rule for inverses

Function's domain becomes inverse's range (and vice versa)

Straight line function form

y=ax+qy = ax + q

Exponential function form

y=bxy = b^x where b>0b > 0 and b≠1b \neq 1

Inverse of exponential function y=bxy = b^x

y=log⁡bxy = \log_b x

Logarithmic power law

log⁡axb=blog⁡ax\log_a x^b = b \log_a x

Logarithmic product law

log⁡axy=log⁡ax+log⁡ay\log_a xy = \log_a x + \log_a y

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