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composit function

substitution of one function into another

f(g(x))

Function denotation

(f o g)

how to show that two composite functions are equal

simplify both equations, if they come out with the same simplified form, than they are equal

What is the domain of a composite function

Domain is the set of all numbers x in the domain of g such that g(s) is in the domain of f

Denotation of f + g (where f and g are functions)

(f+g)(x) = f(x) + g(x)

Denotation of f-g (where f an g are functions)

(f-g)(x) = f(x) - g(x)

Denotation of f multiplied by g (where f and g are functions)

Denotation of f/g (where f and g are functions)

vertical shift (up)

Vertical shift (down)

Horizontal shift (left)

Horizontal shift (right)

reflection about the x-axis

piece-wise function

f(x)= (x-3)^{2}=4 What is the base function

Linear function

constant function

identity function

Square function

Cube function

reciprical function

absolute value function

Greatest integer function

step function

average rate of change

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