pre algebra lesson 8-1
TRANSCRIPT
Relations and Functions
Objective: To use tables and graphs to represent relations and functions.
5-Minute Check
Solve each equation or inequality.1. 3x – 2 = 13
5-Minute Check
Solve each equation or inequality.1. 3x – 2 = 13 x = 5
5-Minute Check
Solve each equation or inequality.1. 3x – 2 = 13 x = 5
2. 6 – 5x = 21
5-Minute Check
Solve each equation or inequality.1. 3x – 2 = 13 x = 5
2. 6 – 5x = 21 x = -3
5-Minute Check
Solve each equation or inequality.1. 3x – 2 = 13 x = 5
2. 6 – 5x = 21 x = -3
3. (2x + 7)/3 = x + 3
5-Minute Check
Solve each equation or inequality.1. 3x – 2 = 13 x = 5
2. 6 – 5x = 21 x = -3
3. (2x + 7)/3 = x + 3 x = -2
5-Minute Check
Solve each equation or inequality.1. 3x – 2 = 13 x = 5
2. 6 – 5x = 21 x = -3
3. (2x + 7)/3 = x + 3 x = -2
4. -12x > -24
5-Minute Check
Solve each equation or inequality.1. 3x – 2 = 13 x = 5
2. 6 – 5x = 21 x = -3
3. (2x + 7)/3 = x + 3 x = -2
4. -12x > -24 x < 2
5-Minute Check
Solve each equation or inequality.1. 3x – 2 = 13 x = 5
2. 6 – 5x = 21 x = -3
3. (2x + 7)/3 = x + 3 x = -2
4. -12x > -24 x < 2
5. 7x < 2x – 25
5-Minute Check
Solve each equation or inequality.1. 3x – 2 = 13 x = 5
2. 6 – 5x = 21 x = -3
3. (2x + 7)/3 = x + 3 x = -2
4. -12x > -24 x < 2
5. 7x < 2x – 25 x < -5
Relations and Functions
A Relation is a set of ordered pairs. The set of the first coordinates is called the domain of the relation. The set of the second coordinates is called the range of the relation.
Relations and Functions
Example:x y
-4 5
-2 6
0 2
Relations and Functions
Example:x y
-4 5
-2 6
0 2Domain: {-4, -2, 0}
Relations and Functions
Example:x y
-4 5
-2 6
0 2Domain: {-4, -2, 0}
Range: {5, 6, 2}
Relations and Functions
A Function is a relation in which each element of the domain is paired with exactly one element in the range.
Relations and Functions
Example:
x y
-4 5
-2 6
0 2
1 7
3 -5
Relations and Functions
Example:
x y
-4 5
-2 6
0 2
1 7
3 -5
Relations and Functions
Example:
x y
-4 5
-2 6
0 2
1 7
3 -5
Relations and Functions
Example:
x y
-4 5
-2 6
0 2
1 7
3 -5
Relations and Functions
Example:
x y
-4 5
-2 6
0 2
1 7
3 -5
Relations and Functions
Example:
x y
-4 5
-2 6
0 2
1 7
3 -5
Relations and Functions
Example:
x y
-4 5
-2 6
0 2
1 7
3 -5
Relations and Functions
Example:
x y
-4 5
-2 6
0 2
1 7
3 -5
The vertical line test can be used to determine if the relation is a function. Use a straight edge moved slowly across the graph to see if two point touch the edge at the same time. This is a true test for all functions.
Relations and Functions
Example:
x y
3 -4
-1 7
-6 -8
1 11
4 13
5.
Relations and FunctionsRelations and Functions
Example:
x y
3 -4
-1 7
-6 -8
1 11
4 13
Domain: {-6,-1,1,3,4}
Range: {-8,-4,7,11,13}
Is this relation a function?
Example:
x y
0 -2
-2 1
3 -2
-4 4
1 -3
6.
Example:
x y
0 -2
-2 1
3 -2
-4 4
1 -3
Domain: {-4,-2,0,1,3}
Range: {-3,-2,1,4}
6.
Is this relation a function?
Example:
x y
0 4
-1 4
-1 3
-1 0
5 1
7.
Example:
x y
0 4
-1 4
-1 3
-1 0
5 1
7.
Domain {-1,0,5}
Range {0,1,3,4}Is this relation a function?