PROPERTIES OF NUMBERS PROPERTIES OF EQUALITY PROPERTIES OF

PROPERTIES OF NUMBERS

PROPERTIES OF EQUALITY

ADDITION PROPERTIES

MULTIPLICATION PROPERTIES

COMMUTATIVE PROPERTY

ASSOCIATIVE PROPERTY

DISTRIBUTIVE PROPERTY

EXAMPLE 1 USF Bulls Baseball Tickets (a. ) A group of 7 adults and 6 children are going to a University of South Florida Bulls baseball game. Use the Distributive Property to write and evaluate an expression for the total ticket cost. Ticket Cost ($) Adult Single Game 5 Children Single Game (12 and under) 3 Groups of 10 or more Single Game 2 Senior Single Game (65 and over) 3

EXAMPLE 1 CONTINUED. . . USF Bulls Baseball Tickets (b. ) A group of 3 adults, an 11 -year old, and 2 children under 10 years old are going to a baseball game. Write and evaluate an expression to determine the cost of tickets for the group. Ticket Cost ($) Adult Single Game 5 Children Single Game (12 and under) 3 Groups of 10 or more Single Game 2 Senior Single Game (65 and over) 3

EXAMPLE 2

EXAMPLE 2 CONTINUED. . .

LIKE TERMS AND SIMPLEST FORM

EXAMPLE 3

WRITE AND SIMPLIFY EXPRESSIONS

(b. ) Simplify the expression, and indicate the properties used. Original expression Distributive property Substitution Commutative property Substitution

(b. ) Simplify the expression, and indicate the properties used. Original expression Distributive property Substitution Commutative property Substitution

RELATIONS

VOCABULARY

MORE VOCABULARY. . . Mapping: illustrates how each element of the domain is paired with an element in the range Domain: Range: the set of the first numbers of the ordered pairs, x-values the set of the second numbers of the ordered pairs, y-values

WAYS TO REPRESENT RELATIONS

EXAMPLE 1 INPUTS OUTPUT S -4 -1 3 2 -2 1

EXAMPLE 1 CONTINUED. . . (b. ) Determine the domain and range. Domain: Range: 4, 3, -2 -1, 2, 1

MORE VOCABULARY Independent variable: the value of the variable that determines the output, the x-value Dependent variable: the value of the variable that is dependent upon the value of the independent variable, the y-value

IDENTIFY THE INDEPENDENT AND DEPENDENT VARIABLES (a. ) The air pressure inside a tire increases with the temperature. Independent: Dependent: the temperature air pressure of a tire (b. ) As the amount of rain decreases, so does the water level of the river. Independent: Dependent: amount of rain water level of the river

ANALYZE GRAPHS (a. ) The longer you ride the bike, the farther you travel (b. ) The farther you travel to school, the longer your drive (c. ) As time increases, the more income you acquire

FUNCTION NOTATION

Function notation: equations that are functions can be represented using different notation

range domain

FUNCTION VALUES

FUNCTIONS

VOCABULARY Function: a relation in which each element of the domain is paired with exactly one element of the range (a. ) (b. )

DETERMINE WHETHER EACH RELATION IS A FUNCTION. . . (a. ) (b. ) (c. )

DISCRETE VS. CONTINUOUS Discrete function: A function where not all input/domain/xvalues are represented, only certain values are represented, points are NOT connected by a line or curve Continuous function: A function where ALL input/domain/xvalues are represented, all points are connected by a line or curve

EXAMPLE 1: A bird feeder will hold up to 3 quarts of seed. The feeder weighs 2. 3 pounds when empty and 13. 4 pounds when full. (a. ) Make a table that shows the bird feeder with 0, 1, 2, and 3 quarts of seed in it weighing 2. 3, 6, 9. 7, and 13. 4 pounds, respectively. Quarts of Seed Weight of Bird Feeder (pounds) 0 2. 3 1 6 2 9. 7 3 13. 4

EXAMPLE 1 CONTINUED. . . (b. ) Determine the domain and range of the function. (c. ) Write the data as a set of ordered pairs then graph the data. Ordered pairs: Domain: 0, 1, 2, 3 {(0, 2. 3), (1, 6), (2, 9. 7), (3, 13. 4)} Range: 2. 3, 6, 9. 7, 13. 4 Graph: (d. ) State whether the function is discrete or continuous. Explain your reasoning. The function is discrete since the person is adding WHOLE numbers of seed to the bird feeder.

How can you tell if a graph shows a function? Vertical Line Test: if a vertical line intersects the graph in more than one place, then the graph (relation) is not a function