Math 12 Principles A1 Notes: Review Relations, Functions, Domain and Range, and Function
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MATH 12 PRINCIPLES A1 NOTES: REVIEW RELATIONS, FUNCTIONS, DOMAIN AND RANGE, AND FUNCTION NOTATION
A. RELATION: A set of ordered pairs in which one value depends on the other value.
A relation can be represented in several ways: 1) as a set of ordered pairs 2) As a table of values
3) as a graph 4) as an equation
B. DOMAIN AND RANGE 1. Domain: the set of first (independent) 2. Range: the set of second (dependent) values for which a relation is defined. values for which a relation is defined.
Examples:
Relation Domain Range 1,5,3,6 x -5 -5 2 y 3 1 0
1 Relation Domain Range y x 2 y x 1 y x y x 2 3 y x 3 1 y 1 x 2
B. FUNCTION: A relation in which there is only one second value for each first value.
Function Example Non-Function Example
Equation: y x 2 Equation: x y 2
Ordered Pairs: Ordered Pairs:
x -3 -2 -1 0 1 2 3 x y y -3 -2 -1 0 1 2 3
Equation Test (Ordered Pair Test) for a Function: If a value of ___ can be found which produces more than ___ value of ____ in the equation, then the equation ______represent a ______. If there are no values of x which produce more than ____ value of ____, then the equation does represent an ______.
Graphing Test (Vertical Line Test) for a Function: If no two points on the graph of a relation can be joined with a vertical line, then the graph represents a function.
2 C. FUNCTION NOTATION i) for Equations Eg 1) if f (x) 3x 2 2x 5 , evaluate: a) f (2) b) f (2)
c) f (x 1) (in simplest form) d) 2 f (x) 1 (in simplest form)
e) Find a such that f (a) 0
Eg 2) If f (x) 3x 2 and g(x) x 2 , determine: a) f (g(x)) b) g( f (x))
c) f ( f (x)) d) g(g(x))
ii) for Graphs
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The function y f (x) is graphed above. 1) Determine: 2) Solve for x: a) f (0) b) f (8) a) f (x) 0
b) f (x) 1
Homework: A1 worksheet #(1,2)ace,4a,8bdfhil,10bce,11a-d,fh,12be,13cd,14all,15a- d,16a-f
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