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

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

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

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.

5. 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). -4
RANGE : The set of output values (the y’s).

6. 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.

7. FUNCTION NOTATION : A function like y = 2x + 7 can be expressed as f(x) = 2x 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

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

9. 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