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 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 =

MULTIPLICATION PROPERTY OF EQUALITY For all real numbers a, b, and c, if a = b, then ac = bc and ca = cb 2218 = 1822

Solve the equation q + 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 > > 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

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.

THE END