1. Defn: A relation is a set of ordered pairs. Domain: The values of the 1 st component of the ordered pair. Range: The values of the 2nd component of the ordered pair. 3.5 – Introduction to Functions

2. xy 13 25 -46 14 33 xy 42 -38 61 9 56 xy 23 57 38 -2-5 87 State the domain and range of each relation. 3.5 – Introduction to Functions

3. Defn: A function is a relation where every x value has one and only one value of y assigned to it. xy 13 25 -46 14 33 xy 42 -38 61 9 56 xy 23 57 38 -2-5 87 functionnot a function function State whether or not the following relations could be a function or not. 3.5 – Introduction to Functions

4. Functions and Equations. xy 0-3 57 -2-7 45 33 xy 24 -24 -416 39 -39 xy 11 1 42 4-2 00 function not a function State whether or not the following equations are functions or not. 3.5 – Introduction to Functions

5. Vertical Line Test Graphs can be used to determine if a relation is a function. If a vertical line can be drawn so that it intersects a graph of an equation more than once, then the equation is not a function. 3.5 – Introduction to Functions

6. x y The Vertical Line Test xy 0-3 57 -2-7 45 33 function 3.5 – Introduction to Functions

7. x y xy 24 -24 -416 39 -39 The Vertical Line Test function 3.5 – Introduction to Functions

8. x y xy 11 1 42 4-2 00 The Vertical Line Test not a function 3.5 – Introduction to Functions

9. Find the domain and range of the function graphed to the right. Use interval notation. x y Domain: Domain Range: Range [ – 3, 4] [ – 4, 2] Domain and Range from Graphs 3.5 – Introduction to Functions

10. Find the domain and range of the function graphed to the right. Use interval notation. x y Domain: Domain Range: Range (– ,  ) [– 2,  ) Domain and Range from Graphs 3.5 – Introduction to Functions

11. Function Notation Shorthand for stating that an equation is a function. Defines the independent variable (usually x) and the dependent variable (usually y). 3.6 – Function Notation

12. Function notation also defines the value of x that is to be use to calculate the corresponding value of y. f(x) = 4x – 1 find f(2). f(2) = 4(2) – 1 f(2) = 8 – 1 f(2) = 7 (2, 7) g(x) = x 2 – 2x find g(–3). g(–3) = (-3) 2 – 2(-3) g(–3) = 9 + 6 g(–3) = 15 (–3, 15) find f(3). 3.6 – Function Notation

13. Given the graph of the following function, find each function value by inspecting the graph. f(5) = 7 x y f(x)f(x) f(4) = 3 f(  5) = 11 f(  6) = 66 ● ● ● ● 3.6 – Function Notation