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CHAPTER 2
SECTION 2-1
PATTERNS AND
ITERATIONS
SEQUENCE
An arrangement of
numbers in a particular
order. The numbers are
called terms and the
pattern is formed by
applying a rule.
EXAMPLES OF
SEQUENCES
0, 2, 4, 6, ___, ___, ___
1, 4, 9, 16, ___, ___,___
EXAMPLES OF
SEQUENCES
2, 8, 14, 20, ___, ___, ___
1, -2, 4, -8, ___, ___,___
EXAMPLES OF
SEQUENCES
4, 12, 20, 28, ___, ___, ___
2, 6, 18, 54, ___, ___,___
SECTION 2-2
THE COORDINATE
PLANE, RELATIONS
AND FUNCTIONS
COORDINATE PLANE
Consists of two
perpendicular number
lines, dividing the plane
into four regions called
quadrants.
X-AXIS - the horizontal
number line
Y -AXIS - the vertical number
line
ORIGIN - the point where the
x-axis and y-axis cross
ORDERED PAIR - an unique
assignment of real numbers
to a point in the coordinate
plane consisting of one xcoordinate and one ycoordinate
(-3, 5), (2,4), (6,0), (0,-3)
RELATION – set of ordered
pairs
DOMAIN – the set of all
possible x-coordinates
RANGE – the set of all
possible y-coordinates
MAPPING – the
relationship between the
elements of the domain
and range
FUNCTION – set of
ordered pairs in which
each element of the
domain is paired with
exactly one element in
the range
SECTION 2-3
LINEAR FUNCTIONS
ABSOLUTE VALUE – the
distance of any real
number, x, from zero on
the number line.
Absolute value is
represented by |x|
|6| = 6, |-6| = 6
LINEAR FUNCTIONS
equations in two variables
that can be written in the
form y = ax + b. The graph
of such equations are
straight lines.
CONSTANT FUNCTION
special linear function where
the domain consists of all
real numbers and where the
range consists of only one
value
y= 2, y = -1, y=3, y= -3
SECTION 2-4
SOLVE ONE-STEP
EQUATIONS
ADDITION PROPERTY
OF EQUALITY
For all real numbers a,
b, and c, if a = b, then
a + c = b + c and
c+a=c+b
22 + 18 = 18 + 22
MULTIPLICATION
PROPERTY OF
EQUALITY
For all real numbers a,
b, and c, if a = b, then
ac = bc and ca = cb
22•18 = 18•22
Solve the equation
q + 18 = 32
-18 = -18
q = 14
SECTION 2-5
SOLVE MULTI-STEP
EQUATIONS
Isolate the variable by:
a. Using the addition
property
b. Using the multiplication
property
SOLVE: 4x + 3 = 15
SOLVE: 4(x – 2) = 3
SOLVE: -3(d – 5) = 18
SECTION 2-6
SOLVE LINEAR
INEQUALITIES
ADDITION PROPERTY
OF INEQUALITY
For all real numbers a,
b, and c, if a < b, then
a+c<b+c
if a > b, then
a+c>c+b
MULTIPLICATION
PROPERTY OF
INEQUALITY
For real numbers a, b,
and positive number c, if a >
b then ac > bc and ca >
cb or if a <b, then
ac < bc and ca < cb
MULTIPLICATION
PROPERTY OF
INEQUALITY
For all real numbers a, b, and
when c is negative,
if a > b, then
ac < bc and ca < cb
or if a < b, then
ac > bc and ca > cb
EXAMPLE
If a = 70, b = 50, and c =
10 then
a + c > b + c or
70 + 10 > 50 + 10
80 > 60
EXAMPLE
If a = 2, b = 5, and c = -10
then
2<5
2(-10) > 5(-10)
-20 > -50
REMEMBER
When you multiply or
divide both sides of an
inequality by a negative
number REVERSE the
sign.
SOLVING INEQUALITIES
Example
3x + 10 < 4
SOLVING INEQUALITIES
Example
23 ≥ 8 - 5y
Half-Plane – a graph of a
solution of a linear
inequality in two
variables
Boundary – the edge of
the half-plane
Open Half-Plane – does
not include the boundary
as part of the solution
Closed Half-Plane – does
include the boundary as
part of the solution
GRAPHING INEQUALITIES
x+y≥4
(0,4),(4,0)
SECTION 2-7
DATA AND MEASURES OF
CENTRAL TENDENCY
POPULATION – entire
group or collections of
things
SAMPLE
a representative part of
the population
FREQUENCY TABLE – a
common way to
organize data
MEASURES OF CENTRAL
TENDENCY
MEAN – is the sum of the
data divided by the number
of data
MEDIAN – is the middle
value of the data
MODE – is the number
that occurs most in the
set of data
RANGE – is the
difference between the
highest and lowest values
of the data
SECTION 2-8
DISPLAY DATA
STEM-AND-LEAF PLOT is
another way to organize
data where the leaf is the
rightmost digit of the
number and the stem is the
remaining digits.
18, 19
20, 22,..
30, 32,…
40,42,…
56
66
OUTLIERS –numbers that
are much smaller or larger
than the rest of the data
CLUSTER –a large
grouping of data about
particular values
GAP – spaces between
clusters and outliers data
HISTOGRAM is a type of
bar graph used to display
data. The height of the bars
of the graph are used to
measure frequency.
Histograms are used to
display data that have been
grouped into intervals.
HISTOGRAM
90
80
70
60
50
East
West
North
40
30
20
10
0
1st Qtr
2nd Qtr
3rd Qtr
4th Qtr
BOX-and-WHISKERS PLOT
Another way to organize
data by grouping the data
into quartiles.
DEFINITIONS
QUARTILE – is another way
to organize data by grouping
the data into four equal parts
INTERQUARTILE RANGE
– is the difference between
the first and third quartiles.
DEFINITIONS
WHISKERS – lines drawn
from the ends of the boxes to
the least and greatest values.
OUTLIERS – data that are at
least 1.5 times the
interquartile range below the
first quartile.
50
55 60
65
70
THE END