DRILL (4 HOURS) (20 dollars) (River Paddlers) The graph below shows the cost (c), in dollars, to rent a boat for h hours at two boat companies. At what number of hours will the cost to rent a boat be the same at both companies? 2) What would be the cost (in dollars) for the boat rentals when the price is the same for each company? 3) Which company is cheaper for a 6 hour rental? (4 HOURS) (20 dollars) (River Paddlers)

Algebra I Functions Objective: SWBAT identify a relation as a function from a set of points, table, mapping or graph.

Textbook Definitions Into Our Definitions A Relation is a set of ordered pairs. The set of the first coordinates is called the domain of the relation. The set of the second coordinates is called the range of the relation. A Function is a relation in which each element of the domain is paired with exactly one element in the range.

Definitions Relation: A relation is any set of ordered pairs. Ex: {(-2,3) (3,-8) (5,7) (5,10)} Function: A function is a relation where each x-value (input) corresponds to exactly one y-value (output). Ex: {(-2,3) (3,-8) (5,7) (8,10)}

Examples {(2, 4) (3, 5) (3, 6) (7, 9)} 2) {(2, 4) (4, 5) (6, 8) (7, 9)} 3) {(1, 2) (3, 5) (7, 6) (8, 9)} 4) {(2, 4) (8, 5) (8, 6) (11, 9)} 5) {(0, 1) (1, 1) (2, 1) (3, 1)} Not a Function Function Function Not a Function Function

Relations vs. Functions (Tables) x y -4 5 -2 6 2 1 7 3 -5 x y -1 5 6 2 3 7 4 -5 x y -2 5 -1 6 2 3 7 15

Relations vs. Functions (Mapping)

Vertical Line Test What type of lines would pass through the x-axis every time? (Horizontal or Vertical) The vertical line test says: if you can draw a vertical line through more than one point on a graph, then it is NOT a function.

A Function or Not A Function, That Is The Question!!

Class Activity You must create one graph that is a function and then one graph that is not a function and you will put them up on the board under the appropriate heading.