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composit function

substitution of one function into another

f(g(x))

Function denotation

(f o g)

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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)

(fg)(x) = f(x)* times* g(x)

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

(f/g)(x) = f(x) / g(x)

vertical shift (up)

add k to each y-cordinate of y=f(x) and raise the graph of f by k units

y=f(x) + k

Vertical shift (down)

subtract k from each y-cordinate of y=f(x) and lower the graph of f by k units

y=f(x) - k

Horizontal shift (left)

Subtract h from each x-cordinate of y=f(x) and shift the graph of f to the left h units

y=f(x-h)

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Horizontal shift (right)

Add h to each x-cordinate of y=f(x) and shift the graph of f to the right h units

y+f(x+h)

reflection about the x-axis

multiply each y-cordinate of y=f(x) by -1, reflect the graph of f about the x-axis

y=-f(x)

multiply each x-cordinate of y=f(x) by -1, reflect the graph of f about the y-axis

y=f(-x)

piece-wise function

when a function is defined by more than one operation

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

the base function is x^{2}

Linear function

f(x)=mx+b

a straight line that passes the vertical line test

constant function

f(x)=b

a strait horizontal line

identity function

f(x)=x

Square function

f(x)=x^{2}

looks like a U

Cube function

f(x)=x^{3}

looks kindave like and S

reciprical function

f(x)= 1/x

looks like a half moon facing away from the origin in the 2cd and 3rd quarters of the graph

absolute value function

f(x) IxI

looks like a V

Greatest integer function

f(x)=int(x)=greatest integer less than or equal to one

step function

another name for the greatest integer function

average rate of change

the slope of two points (otherwise known as the slope of the secant line)

f(x)-f(c)

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x-c

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