ALGEBRA I - SECTION 4-6 (Formalizing Relations and Functions) @ SECTION 4-6 : FORMALIZING RELATIONS and FUNCTIONS

RELATION : a set of ordered pairs (domain, range). Examples : FUNCTION : a relation where the x’s do not repeat. Examples :

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

ALGEBRA I - SECTION 4-6 (Formalizing Relations and Functions) 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.

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) Tell whether each relation is also a function 5) 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

FUNCTION NOTATION : A function like y = 2x + 7 can be expressed as f(x) = 2x + 7. f(x) is read “f of x”. 6) For f(x) = -3x + 2, what is the output for the input a) -4 Answer : 14 b) 0 Answer : 2 Answer : 1.4 c) 0.2

7) The domain for f(x) = -3x + 5 is {-2, 0, 2, 4}. What is the range?

ANSWERS domain 0 < q < 3 range 0 < A < 300 8) Caitlin has 3 quarts of paint to paint the trim of his house. A quart of paint covers 100 ft2. The function A(q) = 100q represents the area, A(q), in square feet that q quarts of paint can cover. What domain and range is reasonable for this function? Graph the function. area ANSWERS domain 0 < q < 3 range 0 < A < 300 quarts