precalc

parent functions

constant, linear, identity, quadratic, cubic, absolute, cube root, and reciprocal

constant function

f(x)=c

C= real #

d=R

r= all reals

linear

F(x)=mx+b

all reals

identity

F(x)=x

m=1

x=0

all reals

quadratic

f(x)=x^2

(0,0)

opens up

square root

f(x)=square root of x

cubic

f(x)=x^3

(0,0)

cube root

f(x)= ^3square root

anchor=(0,0)

absolute

f(x)= |x|

reciprocal

f(x)=1/x

asymptote

boundary line

forces graph to one side

greatest integer

f(x)= int x

rigid transformation

move parent function template th a new location

non rigid

template is stretched or compressed

vert flip

shift up or down

horizon flip

shift left or right

horizon shift

f(x-c)

f(x+c)

negative inside f(-x)

vert shift

f(x)-c

f(X)+c

negative outside -f(x)

domain of a function

the implied domain of any function is all reals

add

f+g

(f+g)x

subtract

f-g

mult

fg

divide

f/g

g(x) can't =0

one-to-one function

function where no RANGE values repeat

synthetic division

way to divide ploynomials that fit a specific criteria

max of TPs

degree - 1

rational functions

functions with variables in denominator