Exam 1 Flashcards
(64 cards)
define relation
set of ordered pairs
define domain
set of the first components of the ordered pairs
x
input
define range
set of the second components of ordered pairs
y
output
define range
set of the second components of ordered pairs
y
output
2 ways to express relations
equations
graphs
define function
a relation where each domain value (x) is paired with only one range value (y)
in function equations, the y value must be able to be…
isolated on one side
raised to the first power only
on graphs, a function must pass the ….
vertical line test
any vertical line you could possibly draw on the plane must only intersect the graph one time
non-example of a function
circle
function notation
f(x) = y
set notation for “y is greater than or equal to 0”
{y|y ≥ 0}
“ | ” means…
“such that”
define interval
single unbroken set of numbers in a line
steps of using interval notation
list leftmost & rightmost boundaries w/ comma between
check if boundaries are part of interval & use ( ) or []
in interval notation, “( )” means…
that boundary is not included
in interval notation, “[]” means…
that boundary is included
if there is no upper or lower boundary, use…
(+/- oo)
if you consider 2 intervals as part of the same set…
use a union
U
ex. (4, oo) U [0, 3)
define natural numbers
1, 2, 3, 4, 5, 6….
no zero
no negatives
no fractions
define whole numbers
naturals + zero
no negatives
no fractions
define integers
whole numbers + negatives
no fractions
define rational numbers
integers and fractions involving integers
includes terminating & repeating decimals
define irrational numbers
cannot be written as a fraction of integers
includes non-repeating, non-terminating decimals
ex. pi, square root of 2, etc
define real numbers
union of rational & irrational numbers
