Identifies real-life situations using functions, including piece-wise functions<|>Represents real-life situations using functions, including piece-wise functions<|>Appreciates the use of functions in representing real-life situations
Example
{(a,1), (c,5), (h,6), (m,9), (z,11)}
Relation
A set of ordered pairs, such that to each X there corresponds at least one Y
Domain (D or X)
The set of all inputs or the first set of elements in the ordered pairs
Range (R or Y)
The set of all outputs or the second elements in the ordered pair
Function
A relation with the property that for each input there is exactly one output. For every X there corresponds a unique or exactly one Y
Domain (D or X)
(a, c, h, m, z)
Range (R or Y)
(1, 5, 6, 9, 11)
All functions are relations but not all relations are functions
Ways to Determine Whether a Relation is a Function or Not
1. Listing of ordered pairs
2. Arrow Diagram
3. Table
4. Equation
5. Graph
If there are two or more ordered pairs with the same first element, then the relation is not a function
Example 1
{(1,6), (2,2), (3,4), (4,8), (5,10)}
If the first set is mapped to 2 or more in the second set, then it is not a function
Example 2
{(1,1), (2,4), (3,1), (4,16)}
Example 3
{(1,1), (1,4), (2,4), (3,5)}
If the exponent of the dependent variable y is an odd integer, then it is a function
If the first component is not constant, then it is a function
