2. Bellringer Graph each ordered pair on the coordinate plane.
1. (–4, –8)
2. (3, 6)
3. (0, 0)
4. (–1, 3)
Evaluate each expression for x = –1, 0, 2, and 5.
6. x –2x x |x – 3|

3. Solutions
6. x + 2 for x = –1, 0, 2, and 5:
1, 2, 4, 7
7. –2x + 3 for x = –1, 0, 2, and 5:
5, 3, –1, –7
8. 2x2 + 1 for x = –1, 0, 2, and 5:
3, 1, 9, 51
9. |x – 3| for x = –1, 0, 2, and 5:
4, 3, 1, 2 . . .

4. Chapter 2.1 Relations and Functions
Objective: Students will use tables and graphs to plot points and describe relations and functions

7. Relations Relation – a set of pairs of input and output values
Can be written in ordered pairs (x,y)
Can be graphed on a coordinate plane
Domain – the set of all input values
The x values of the ordered pairs
Range – the set of all output values
The y values of the ordered pairs
When writing domains and ranges:
Use braces { }
Do not repeat values NON-Example: {3,3,5,7,9}

8. Graph the relation {(–3, 3), (2, 2), (–2, –2), (0, 4), (1, –2)}.

9. Try These Problems {(0,4),(-2,3),(-1,3),(-2,2),(1,-3)}
{(-2,1),(-1,0),(0,1),(1,2)}

10. Write the ordered pairs for the relation. Find the domain and range.
{(–4, 4), (–3, –2), (–2, 4), (2, –4), (3, 2)}
The domain is {–4, –3, –2, 2, 3}.
The range is {–4, –2, 2, 4}.

11. Mapping Diagram
Another way to represent a relation (beside traditional graphing)
Links elements of the domain with corresponding elements of the range
How To make a mapping diagram:
Make two lists – place numbers from least to greatest
Domains on the left
Ranges on the Right
Draw arrows from corresponding domains to ranges (x’s to y’s)

12. Make a mapping diagram for the relation {(–1, 7), (1, 3),(1, 7), (–1, 3)}.
Domain
Range -1 1 3 7

13. Try These Problems Make a Mapping Diagram for each relation.
{(0,2),(1,3),(2,4)}
{(2,8),(-1,5),(0,8),(-1,3),(-2,3)} -2 -1 2 1 2 2 3 4 3 5 8

14. Functions
Function – a relation in which each element of the domain is paired with EXACTLY one element of the range
All functions are relations, but not all relations are functions!!!

15. There are several ways to determine if a relation is a function:
Mapping Diagram
If any element of the domain (left) has more than one arrow from it
List of ordered pairs
Look to see if any x values are repeated
Coordinate Plane
Vertical Line Test – If a vertical line passes through more than one point on the graph then the relation is NOT a function.

16. Determine whether each relation is a function.b) -1 2 3 -2 5 -1 3 4 -1 3 5
This is NOT a function because -2 is paired with both -1 and 3.
This is a function because every element of the domain is paired with exactly one element of the range.

17. Try These Problems Determine whether each relation is a function.2 3 4 7 5 6 8 -1 1 -3 7 10
Not a function
Function

18. Vertical Line Test

19. Try These Problems Use the Vertical Line Test to determine whether each graph represents a function.
Not a Function
Function
Not a Function

20. Function Rules
Function Rule – expresses an output value in terms of an input value
Examples:
y = 2x
f(x) = x + 5
C = πd
Function Notation –
f(x) is read as “f of x”
This does NOT mean f times x !!!!
f(3) is read as “f of 3”: It means evaluate the function when x = 3. (plug 3 into the equation)
Any letters may be used C(d) h(t)

21. Find ƒ(2) for each function.
a. ƒ(x) = –x2 + 1
ƒ(2) = – = –4 + 1 = –3
b. ƒ(x) = |3x|
ƒ(2) = |3 • 2| = |6| = 6 9
1 – x
c. ƒ(x) =
ƒ(2) = = = –9 9
1 – 2 –1

22. Try These Problems Find f(-3), f(0), and f(5) for each function
f(x) = 3x – 5
f(-3) = 3(-3) – 5 = -9 – 5 = -14 f(0) = 3(0) – 5 = 0 – 5 = -5 f(5) = 3(5) – 5 = 15 – 5 = 10
f(a) = ¾ a – 1
f(-3) = ¾ (-3) – 1= -9/4 – 4/4 = -13/4 f(0) = ¾ (0) – 1 = 0 – 1 = -1 f(5) = ¾ (5) – 1 = 15/4 – 4/4 = 11/4
f(y) = -1/5 y + 3/5
f(-3) = -1/5 (-3) + 3/5 = 3/5 + 3/5 = 6/5 f(0) = -1/5 (0) + 3/5= 0 + 3/5 = 3/5 f(5) = -1/5 (5) + 3/5 = -5/5 + 3/5 = -2/5

23. Groupwork/Homework Day 1: Day 2: 2.1, page 59 (1-19)
Show all work for function notation problems
Day 2:
Page 59 (22 – 38 even)
Be sure to write each problem – this includes writing out the sets of coordinate pairs and sketching graphs

24. Groupwork/Homework Honors
Section 2.1 page 59 ( odd, )