Graphs & Functions

Function notation, composite and inverse functions, and sketching and transforming graphs.

Functions

$f(x)$ maps inputs to outputs. The domain is the set of allowed inputs; the range the set of outputs.

Composite

fg(x) = f(g(x))

— do

g

first.

Inverse

f^{-1}(x)

reverses

f

: set

y=f(x)

, swap

x

and

y

, rearrange. The graph of

f^{-1}

is the reflection of

f

y=x

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