ALGEBRA II HONORS/GIFTED - SECTION 2-1 (Relations and Functons) @ SECTION 2-1 : RELATIONS and FUNCTIONS

RELATION : a set of ordered pairs (inputs and outputs). Examples : FUNCTION : a relation where the x’s do not repeat. Examples :

Determine if the following graphs represent functions. 1) 2) 3) 4)

ALGEBRA II HONORS/GIFTED - SECTION 2-1 (Relations and Functons) VERTICAL LINE TEST : If you drop a vertical line through any place on a graph, you may touch at most one point on the graph if the graph represents a function.

ALGEBRA II HONORS/GIFTED - SECTION 2-1 (Relations and Functons) REPRESENTING RELATIONS ORDERED PAIRS (-3, 2) (4, 6) (-3, 5) (0, -4) TABLE GRAPH X Y -3 2 4 6 5 -4 MAPPING input output DOMAIN : The set of input values (the x’s). -3 2 4 6 0 5 -4 RANGE : The set of output values (the y’s).

5) According to 2016 census estimates, the four most populous states (in millions) were California (39), Texas (28), Florida (21), and New York (20). The number of U.S. Representatives were CA (53), TX (36), FL (27) and NY (27). Given that the domain is the population and the range is the number of representatives, write the relation as : a) ordered pairs b) a mapping c) a chart d) a graph

6) Tell whether each relation is also a function 6) Tell whether each relation is also a function. Answer yes or no and explain your answer. a) {(0, 0), (2, 4), (-2, 4), (3, 9), (-3, 9)} Answer : yes, no members of the domain repeat. input output b) Answer : no, 6 maps to two elements of the range. 1 -4 0 -2 6 2 8 4

7) For f(x) = -3x + 2, what is the output for the input Answer : 14 b) 0 Answer : 2 c) 0.2 Answer : 1.4

8) A pizza costs $14 with a flat delivery charge of $1.50. a) What function rule models the total cost of pizzas delivered? Answer : C(p) = 14p + 1.50 b) Evaluate for five pizzas. Answer : $71.50