Chapter 2.1 Functions

Functions domain What comes out is “dependent” upon what goes in. range

A function is a relation that has one output for each input A function is a relation that has one output for each input. The input value is called the domain and the output value is called the range. Several ways to show a function. Mapping: Ordered Pairs: Domain: Range: (Jack, $75) (Emiry, $150) (Raylon, $75) Jack Emiry Raylon $75 $100 $150 Graph:

What is NOT a function. Mapping: Ordered Pairs: Domain: Range: (Jack, $75) (Emiry, $150) (Raylon, $75) (Emiry, $100) Jack Emiry Raylon $75 $100 $150 Graph: Use the Vertical Line test on a graph to determine whether the graph is a function. If the vertical line touches the graph in more than one point, then it is NOT a function.

Functions (2,4) (5,6) (9,8) (3,8) (2,4) (5,6) (9,8) (5,8) You only need to look at the x-coordinates when determining functions. If the x-coordinates has the same value more than once then it is NOT a function. (2,4) (5,6) (9,8) (3,8) Function Not a Function (2,4) (5,6) (9,8) (5,8)

Function or Not a Function?

Function Notation: Before: y = mx + b Now: f(x) = mx + b read “f of x” Evaluate each function for the given value of x. y = 3x – 5 ; x = -2 f(-2) = 3x – 5 f(-2) = 3(-2) – 5 f(-2) = -6 – 5 f(-2) = -11 f(x) = 2x² - 3x +4 f(-3) = 2(-3)² - 3(-3) + 4 f(-3) = 31 f(x) = 3x – 5 ; f(-2)

F(x) = Is the point (1, ½) on the graph of f? If x = -1, what is f(x)? What point is on the graph of f? If f(x) = 2, what is x? What is the point on the graph of f?

Finding the domain of a function. “What do we NOT want to happen.” F(x) = x² + 5x g(x) = 3x X² - 4

Finding the domain of a function. “What do we NOT want to happen.” h(x) = √4 – 3x 3 f(x) = √4 – 3x