Exam 1 Flashcards
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
(A + B) + C = A + (B + C)
A(BC) = AB(C)
associativity
A + B = B + A
AB = BA
commutativity
A(B + C) = AB + AC
distribution
A + 0 = A
1A = A
identity
define coefficient
* variable
define expression
terms added & subtracted together
define term
collection of variables & numbers multiplied & divided together
define equation
2 expressions w/ an equal sign between
define linear
describes a term, expression, or equation where…
- each term has one variable or less
- variables are raised only to the first power
define compound inequality
combination of 2 inequality statements
2 types of compound inequalities
intersection
union
define intersection
a set of values present in one set AND the other
define union
set with values present in one set OR the other
which compound inequality has overlap?
which has a gap?
overlap - intersection
gap - union
x = all real numbers in interval notation
(-oo, oo)
what makes linear functions unique?
they have a constant rate of change between inputs & outputs
every linear function has…
a slope
m =
slope
SLOPE EQUATION
what is necessary to calculate slope?
2 ordered pairs
a slope of - ⅔ indicates that…
- the line runs downward (-)
- it takes 2 units in x to move down 3 units in y
to uniquely determine a linear function, we need…
slope
an ordered pair for the function
b =
the initial value of f(x)
f(o)
the y-intercept
LINEAR FUNCTION EQUATION
to find x intercept…
place 0 in for y
to find y intercept…
place 0 in for x
how to generate an ordered pair using slope
rise + a y-value and run + an x-value = an ordered pair
slopes of perpendicular lines
negative reciprocal
formula for vertical lines
x = z
formula for horizontal lines
y = b
product rule
am * an = am+n
zero rule
a0 = 1
quotient rule
am/an = am-n
negative rule (2)
a-n = 1/an
1/a-n = an
power rule (3)
- (am)n = amn
- (ab)n = anbn
- (a/b)n = an/bn
define polynomial
expression made of terms whose variables are raised to natural powers
degree of a polynomial
greatest exponent
leading term
term with the greatest variable
leading coefficient
coefficient of the leading term
shortcuts for full polynomial multiplication
FOIL
each term * each term
