# ALGEBRA I @ SECTION 4-6 : FORMALIZING RELATIONS ALGEBRA I @ SECTION 4-6 : FORMALIZING RELATIONS and RELATION : a set of ordered pairs (domain, range). Examples : FUNCTION : a relation where the xs do not repeat. Examples :

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

2 4 6 -3 5 0 -4 GRAPH

MAPPING input output -3 2 4 6 0 5 DOMAIN : The set of input values (the xs). RANGE : The set of output values (the ys).

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. b) input 1 0 6 8 output

-4 -2 2 4 Answer : no, 6 maps to two elements of the range. 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 b) 0 c) 0.2 Answer : 14 Answer : 2 Answer : 1.4 7) The domain for f(x) = -3x + 5 is {-2, 0, 2, 4}. What is the range? x

f(x) 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. ANSWERS domain range

area 0