CHAPTER 2
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Transcript of CHAPTER 2
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 THE COORDINATE PLANE, PLANE,
RELATIONS AND RELATIONS AND FUNCTIONSFUNCTIONS
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 x-coordinate and one y-coordinate
(-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 propertyb. 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, thenac < bc and ca < cb
or if a < b, thenac > 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 INEQUALITIESExample
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 dataMEDIAN – is the middle value of the data
MODE – is the number that occurs most in the set of dataRANGE – 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, 1920, 22,..30, 32,…40,42,…5666
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
0
10
20
30
40
50
60
70
80
90
1st Qtr 2nd Qtr 3rd Qtr 4th Qtr
East
West
North
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 partsINTERQUARTILE RANGE – is the difference between the first and third quartiles.
DEFINITIONSWHISKERS – 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