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relation
linking/pairing of elements from set A to set B
b. ordered pair
R = {(1,2),(3,4),(5,6),(7,8)}
d. equation
y = 2x
*if unknown values are given for sets A&B, then there are infinite values for x&y
functions
many-to-one or one-to-one
vertical line test
used to determine whether function or not; all possible lines must only intersect the graph ONCE (more than once: not a function)
horizontal line test
one-to-one or many-to-one; at least 1 horizontal line intersecting the graph once: many-to-one
domain of a function
independent variables / set A / x-values
range of a function
dependent variables / set B / y-values
function composition
f of g of x
f(g(x))
f = main
g(x) = substitute (input)
OR function composition g of x
(f ○ g)(x)
quadratic function for inverse functions
ex: h(x) = (x-3)² + 1
vertex: (3,1) → start from (0,0)
inside parenthesis/square root: (+) left, (-) right
outside: (+) up, (-) down
equations of inverse functions
ex: f(x) = 2x + 1
relations in inverse functions
f(x) → f¯¹(x)
o-o → o-o
m-o → m-o
o-m → m-o
(switch)
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