1. Chapter 2.1
Functions

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

3. 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:

4. 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.

5. 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)

6. Function or Not a Function?

7. 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)

9. 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?

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

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