1. 2-1: Graphing Linear Relations and Functions
Objectives:
Understand, draw, and determine if a relation is a function.
Graph & write linear equations, determine domain and range.
Understand function notation
NOTES CH 2.1 Functions

2. Relations & Functions- I. VOCAB
Relation: a set of ordered pairs
Domain: the set of x-coordinates (all the values that x can be!)
Range: the set of y-coordinates (all the values that y can be!)
**When writing the domain and range, do not repeat values.**
NOTES CH 2.1 Functions

3. Relations and Functions
EX 1:
Given the relation:
{(2, -6), (1, 4), (2, 4), (0,0), (1, -6), (3, 0)}
State the domain:
D: {0,1, 2, 3}
State the range:
R: {-6, 0, 4}
NOTES CH 2.1 Functions

4. Relations and Functions II. Representations
Relations can be written in several ways: ordered pairs, table, graph, or mapping.
We have already seen relations represented as ordered pairs.
NOTES CH 2.1 Functions

5. Table EX 2: {(3, 4), (7, 2), (0, -1), (-2, 2), (-5, 0), (3, 3)}
NOTES CH 2.1 Functions

6. Mapping
Create two ovals with the domain on the left and the range on the right.
Elements are not repeated.
Connect elements of the domain with the corresponding elements in the range by drawing an arrow.
NOTES CH 2.1 Functions

7. Mapping EX 3: {(2, -6), (1, 4), (2, 4), (0, 0), (1, -6), (3, 0)} D R 2
 -6 4 2 1 3
NOTES CH 2.1 Functions

8. Mapping diagrams Make an mapping diagram.
EX 4: {(1, 2), (-1, 4), (0, 2), (4, -7)}
See board.
EX 5: {(2, 3), (-1, -5), (2, 6)}
See board.
NOTES CH 2.1 Functions

9. III. Functions
A function is a relation in which the members of the domain (x- values) DO NOT repeat.
So, for every x-value there is only one y-value that corresponds to it.
y-values can be repeated.
NOTES CH 2.1 Functions

10. Do the ordered pairs represent a function? Make a mapping diagram.
EX 6. {(3, 4), (7, 2), (0, -1), (-2, 2), (-5, 0), (3, 3)}
No, 3 is repeated in the domain.
EX 7. {(4, 1), (5, 2), (8, 2), (9, 8)}
Yes, no x-coordinate is repeated.
NOTES CH 2.1 Functions

11. When given a graph, is it a function?
Vertical Line Test: If a vertical line is passed over the graph and it intersects the graph in exactly one point, the graph represents a function.
Domain: all values x can be. “Where does the graph stop to the left and to the right?”
Range: all values y can be. “ Where does the graph stop looking up and down?”
NOTES CH 2.1 Functions

12. Does the graph represent a function? Name the domain and range.x y
Yes
D: all reals
R: all reals
R: y ≥ -6
EX 8 x y
EX 9
NOTES CH 2.1 Functions

13. Does the graph represent a function? Name the domain and range.x y No
D: x ≥ 1/2
R: all reals
D: all reals
EX 10 x y
EX11
NOTES CH 2.1 Functions

14. Does the graph represent a function? Name the domain and range.x y
Yes
D: all reals
R: y ≥ -6 No
D: x = 2
R: all reals
EX12 x y
EX 13
NOTES CH 2.1 Functions

15. IV. Function Notation
When we know that a relation is a function, the “y” in the equation can be replaced with f(x).
f(x) is simply a notation to designate a function. It is pronounced ‘f’ of ‘x’.
The ‘f’ names the function, the ‘x’ tells the variable that is being used.
NOTES CH 2.1 Functions

16. Value of a Function
Since the equation y = x - 2 represents a function, we can also write it as f(x) = x - 2.
EX 14. Find f(4):
f(4) = 4 - 2
f(4) = 2
NOTES CH 2.1 Functions

17. Value of a Function EX 15. If g(s) = 2s + 3, find g(-2).
=-4 + 3
= -1
g(-2) = -1
NOTES CH 2.1 Functions

18. Value of a Function EX 16. If h(x) = x2 - x + 7, find h(2c).
h(2c) = (2c)2 – (2c) + 7
= 4c2 - 2c + 7
NOTES CH 2.1 Functions