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linear relations & functions (functions (a type of relation, a…
linear relations & functions
relations
an association between two quantities, and can be represented as an equation, graph, table of values, or ordered pairs
discrete data
only show the points as dots because any values in between are irrelevant
continuous
a continuous line shown through the points, as every point has meaning
linear relations
have graphs that are straight lines
variables that have a degree of 1
(the sum of the values of the exponents)
the x and y variables increase or decrease by evenly spaced intervals
non-linear relations
don't have degrees of 1
x and y increase or decrease by different amounts
domain & range
used to describe the parametres of a set of numbers
domain: the set of all possible values for the independant variable in a relation
range: the set of all possible values for the dependant variable in a relation
ways to show domain range
set notation (most tricky)
I means "such that"
{ } are the types of brackets used for a set
∈ means "an element of"
interval notation (medium tricky)
( ) means "up to the end number, not inclusive"
[ ] means "up to the end number inclusive"
a list (least tricky)
used when there are not many number in the set
functions
a type of relation
a relation in which each value of the independant variable is associated with exactly one value of the dependant variable
written in function notation
f(x) = ........
fancier way of writing y, as it's a function of x because the point is somewhere along the line
how to identify if it's a function or not: the vertical line test
slope
the ratio of vertical change to horizontal change
not expressed in units
m = rise / run
0 / x = a horizontal line
x / 0 = an undefined slope
m = y2 - y1 / x2 - x1
arithmetic sequence
sequence: an ordered list of elements
tn = t1 (n - 1) d
t = term
n = the nth term
d = (common) difference