Section 1 – Relations and Functions Chapter 1 Section 1 – Relations and Functions

What’s a relation? A relation is a pairing of one set of numbers to another set of numbers. The domain of a relation is the set of the first group of numbers. The range of a relation is the set of the second group of numbers. Which variables are usually attributed to the domain and range?

Tables and Graphs EX 1: The domain of a relation is all positive integers less than 6. The range of the relation is 3 less x, where x is a member of the domain. Write the relation as a table of values and as an equation. Then graph the relation.

Domain and Range Look at the graph to the right. What is the domain and range of the graph?

More Domain and Range What is the domain and range of the graph below?

Functions A relation is a function if each element of the domain is paired with EXACTLY one element in the range. Tell me if the following sets are functions or not: {(3,0),(4,2),(5,3)} {(2,1),(2,3),(3,4)} {(2,6),(4,6),(6,1)}

Vertical Line Test If you are JUST given a graph (no points), you can still determine whether it represents a relation or a function. This is called the Vertical Line Test. If you can draw a vertical line ANYWHERE on a graph, and it passes through the graph more than once, the graph is NOT a function.

Testing the Vertical Line Test Tell me if the graphs below represent functions or not.

Function Notation f(x) is function notation for ALMOST every function that we will discuss in this class. You can say “f(x)” as “f of x”. Now let’s evaluate some functions.

Evaluating Functions EX 2: Evaluate f(-3) for the function f(x) = 2x3 + 4x – 6 EX 3: Evaluate f(5) for the function f(x) = |3x2 + 5| EX 4: Evaluate f(-2) for the function f(x) = 3x - 4

Domain of Functions Can you tell me the domain of the following functions? EX 5: f(x) = x2/(x-3) EX 6: f(x) = x3 EX 7: g(x) = 1/√(x-4)

Section 1.1 Assignment Chapter 1, Section 1 pgs 10-11 #18-50 evens