lecture sa mat111 1 to payb.pptx - GENERAL MATHEMATICS(MAT 111 Senior High School Grade 11 CHAPTER 1 FUNCTIONS LESSON 1 FUNCTIONS AS MODEL Difference of

# lecture sa mat111 1 to payb.pptx - GENERAL MATHEMATICS(MAT...

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Senior High School Grade 11 GENERAL MATHEMATICS (MAT 111)
CHAPTER 1: FUNCTIONS LESSON 1: FUNCTIONS AS MODEL Difference of relations and functions Relations is a rule that relates values from a set of values(domain) to a second set of values (range) Elements of the domain can be imagined as input to a machine that applies a rule to these inputs to generate one or more outputs. A set of ordered pairs (x, y) Functions is a relation where each element in the domain is related to only one value in the range by some rule. Elements of the domain can be imagined as input to a machine that applies a rule so that each input corresponds to only one output. A set of ordered pairs (x, y) such that no two ordered pairs have the same x-vaue but different y- values.
FUNCTIONS AND RELATIONS AS A TABLE OF VALUES Example 1: which of the following relations are functions? a. f = {(1,2), (2,2), (3,5), (4,5)} b. g = {(1,3), (1,4), (2,5), (2,6), (3,7)} c. h = {(1,3), (2,6), (3,9) . . . , ( n, 3 n)… } Relations f and h
Example 2: which of the following mapping diagrams represent functions?123453591733f5678901g7211113171923h
FUNCTIONS AS A GRAPH IN THE CARTESIAN PLANE The Vertical Line Test A graph represents a function if and only each vertical line intersects the graph at most once.
Example 3: which of the following graphs can be graphs of functions? A B C D
Example 4: which of the following represents a function? a)y = 2x + b)y = c)x2 + y2= d)y e)y 1 1 = =
1 1 = = Identify the domain for each relation using set builder notationdomaina)[-1, 1]b)[-1, +∞]c)(-∞,1) (1, +∞)
1 1 = = If a relation is a function, then y can be replaced with f(x) to denote that the value of y depends on the value of x.functions 1 = =
FUNCTIONS AS REPRESENTATIONS OF REAL-LIFE SITUATIONS