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Transcript
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. 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 0 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) -2 -1 Function ( 3x + 2 ) f(-2) = 3(-2) + 2 Output (y) Ordered pair (x , y) -4 -1 (-2 , -4) (-1 , -1) 2 (0 , 2) 0 f(-1) = 3(-1) + 2 f(0) = 3(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. It will cost her 500 dollars to make the shirts. To make profit, she is selling the shirts at $8 a shirt. Independent variable : Number of T shirts sold (t) Dependent variable : 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