1. Chapter 3
Graphs and Functions

2. Chapter Sections 3.1 – Graphs 3.2 – Functions
3.3 – Linear Functions: Graphs and Applications
3.4 – The Slope-Intercept Form of a Linear Equation
3.5 – The Point-Slope Form of a Linear Equation
3.6 – The Algebra of Functions
3.7 – Graphing Linear Inequalities
Chapter 1 Outline

3. § 3.2
Functions

4. Understand Relations Dependent and Independent Variables
For an equation in variables x and y, if the value of y depends on the value of x, then y is the dependent variable and x is the independent variable.
Relation, Domain, Range
For an equation in variables x and y, if the value of y depends on the value of x, then y is the dependent variable and x is the independent variable.

5. NOT A FUNCTION (Tom can’t be 21 and 22 at the same time)
Recognize Functions
Function
A function is a relation in which each element in the domain corresponds to exactly one element in the range.
Persons
Tom
Bob
Mark
Bill
Ages 21 22 25 20
Persons
Tom
Bob
Mark
Bill
Ages 21 22 25 20
FUNCTION
NOT A FUNCTION (Tom can’t be 21 and 22 at the same time)

6. Use the Vertical Line Test
Graph of Function or Relation
The graph of a function or relation is the graph of its set of ordered pairs.
Vertical Line Test
If a vertical line can be drawn so that it intersects a graph at more than one point, then the graph does not represent a function. If a vertical line cannot be drawn so that it intersects a graph at more than one point, then the graph represents a function.

7. Vertical Line Test
NOT A FUNCTION
FUNCTION
FUNCTION

8. Understand Function Notation
If an equation involving x as the independent variable and y as the dependent variable defines a function, we say y is a function of x and we write y = f(X).
When a function is evaluated, a value is substituted into the function.
f(x) = 3x + 2
f(1) = 3(1) + 2 = 5
Therefore, when x is 1, y is 5. The ordered pair (1, 5) appears on the graph of y = 3x + 2.