2.1: Relations and Functions
2.2: Linear Equations
Relation
5
Ex1) Graph the coordinate points:
4
3
(–3, 3), (2, 2), (–2, –2),
(0, 4), (1, –2)
2
1
-5 -4 -3 -2 -1
1
2
3
4
-1
-2
-3
-4
-5
A relation is a set of pairs of input (x) and output (y) values.
Written: {(–3, 3), (2, 2), (–2, –2), (0, 4), (1, –2)}.
5
Relation
{(–3, 3), (2, 2), (–2, –2), (0, 4), (1, –2)}
Domain – the set of all inputs of a function, x-coordinates,
independent variable
Domain: {-3, -2, 0, 1, 2 }
Range - the set of all outputs of a function, y-coordinates,
dependent variable
Range: { -2, 2, 3, 4 }
Relation
Ex2) Write the ordered pairs for the relation.
Find the domain and range.
Mapping Diagrams
Ex3) {(–3, 3), (2, 2), (–2, –2), (0, 4), (1, –2)}.
Domain
Range
Functions
A function is a relation in which each input value is paired
with only one output value.
Domain (YOU)
Range
(BIRTHDAY)
Functions
A function is a relation in which each input value is paired
with only one output value.
Domain
Range
Domain
2
-2
-1
0
3
5
4
Function?
3
4
7
Function?
Range
5
6
8
Vertical Line Test
Vertical Line Test: If a vertical line passes through at least
two points on the graph, the relation is not a function.
Ex4) {(-2, -1), (0, 3), (-2, 3), (5, 4)}
6
Ex5) {(3, 6), (2, 6), (7, 8), (4, 5)}
9
5
8
4
7
3
2
6
1
-6 -5 -4 -3 -2 -1
-1
-2
-3
5
1 2 3 4 5 6
4
3
2
-4
-5
-6
1
1
2
3
4
5
6
7
8
9
Vertical Line Test
Ex6) Are these relations functions? If so, describe the
domain and range
5
5
5
4
4
4
3
3
3
2
2
2
1
1
1
-5 -4 -3 -2 -1
1
2
3
4
5
-5 -4 -3 -2 -1
1
2
3
4
5
-5 -4 -3 -2 -1
1
-1
-1
-1
-2
-2
-2
-3
-3
-3
-4
-4
-4
-5
-5
-5
2
3
4
5
Function Notation
Function notation f ( x) is read "f of x" or "a function f of x."
y   x 2  3  f ( x)   x 2  3
Ex7) For the function f ( x) above, find f (2) and f (3).
Function Notation
Ex8) The surface area of a cube is a function of the length of a
side of the cube. Write a function for the surface area of the
cube. Find the surface area of the cube with a side 2 inches
long.
What is Slope??
Slope
y
vertical change (rise)
y2  y1
slope 


x horizontal change (run)
x2  x1
Ex4)  2, 2  and  4,2 
Ex5)  2,7  and 8, 6 
Slope (cont.)
y (rise)
slope 
x(run)
What does it mean if the slope is zero?
What does it mean if the slope is Undefined?
2.1: Relations and Functions
2.2: Linear Equations
Homework #9:
Pg 59 #1-29 odd
Pg 67 #11-19 odd