Function Notation Warm Up Determine the Domain and Range of the following set of ordered pairs. Is the set of ordered pairs a function? Why or why not? { (3 , 2) , (4 , 3) , (1 , 4) , (2 , 3) } Remember: The domain of a relation is all the input values or x values. These values are the first numbers in the ordered pairs. The Range of a relation is all the output values or y values. These values are the second numbers in the ordered pairs. Domain: {3, 4, 1, 2} Range: {2, 3, 4, 3} Remember that if a relation is a function, no x value can repeat. Looking at our Domain, do any numbers repeat? NO. So our relation is a function because no x values repeat.

The typical notation for a function is f(x). This is read as “f of x” because it is a Function of X. THIS DOES NOT MEAN f times x.

Tells what number to plug in. Function Notation Name of the function Tells what number to plug in. f(x) = 3x + 4 { { f(x) means the output of the functions f then the input is x. We often refer to this as y. THE FUNCTION

f(x) = 2x - 1 Input (x) Function ( 2x – 1 ) Output (y) -2 f(-2) = 2(-2) - 1 -5 -1 f(-1) = 2(-1) - 1 -3 f(0) = 2(0) - 1 -1 1 f(1) = 2(1) - 1 1 2 f(2) = 2(2) - 1 3

f(x) = 3x +2 Input (x) Function ( 3x + 2 ) Output (y) Ordered pair (x , y) -2 f(-2) = 3(-2) + 2 -4 (-2 , -4) -1 f(-1) = 3(-1) + 2 -1 (-1 , -1) f(0) = 3(0) + 2 2 (0 , 2) 1 f(1) = 3(1) + 2 5 (1 , 5) 2 f(2) = 3(2) + 2 8 (2 , 8)

Becky is selling Bulldog Shirts at school Becky is selling Bulldog Shirts at school. It will cost her 500 dollars to make the shirts. To make profit, she is selling the shirts at $8 a shirt. Independent variable : Dependent variable : Number of T shirts sold (t) Profit (P) The profit from selling t number of shirts is described by the following function. P( t ) = 8t – 500 Find P(70) P(70) = 8(70) – 500 = 60