Algebra II / trigonometry

rules for function

x-values cant repeat

y-values can repeat

has to pass vertical line test

a linear function

f(x)=mx+b

absolute value

f(x)= |x|

a quadratic function

f(x)=x² 

expotential function

f(x)=a^x

piecewise function

f(x) has different defenitions for x

even functions

symmetric over y-axis

odd function

symetric over (0,0)

(if its upside down its the same)

domain

all possible x’s left+right

range

All possible y’s up +down

what are the domain and range for these types of functions

f(x)=2x-2

f(x)=7x-2

f(x)=3x+5

domain= all real numbers

range= all real numbers

what are the domain and range for these types of functions

f(x)=1/x

f(x)=2/x

f(x)=10/x

domain=all real numbers excluding 0

range= all real numbers excluding 0

²

f(x)=3^x

f(x)=5^x

f(x)=7^x

domain=all real numbers

range=y>0

what are the domain and range for these types of functions

f(x)=-x²+3

domain= all real numbers

range= y<3

f(x)+k is f(x) shifted to the….

up

f(x)-k is f(x) shifted k to the…..

down

f(x+k)  is f(x) shifted k to the…..

left

f(x-k) is f(x) shifted k to the…..

right

direct variation equation

y=kx

as one variable increases so does the other one.

inverse variation equation

y=k/x

as one variable increases the other decreases

(graph is a rectangular hyperbola)

g(f(x)

put f inside g

inverse of f is written as what

f^-1

to find the inverse of a function simply means

switch x and y

(reflection over y=x)