1. Graphing Linear Functions
Chapter 3
Graphing Linear Functions
3.1
Functions
What is a function?
Students will be able to determine whether relations are functions.
Students will be able to find the domain and range of a function.

2. Students will be able to determine whether relations are functions.
A relation pairs inputs with outputs.
When a relation is given as ordered pairs, the x-coordinates are the inputs and the y-coordinates are outputs.
A relation that pairs each input with exactly one output is a function.
Each of the following is a relation.
Determine whether each relation is a function. Explain.
Function; each input has one output
Relation; the input 4 has two outputs
Input, x -2 -1 1 2
Output, y 3 4 5 6 7 8
Relation; the input 0 has two outputs

3. Students will be able to determine whether relations are functions.
A relation that pairs each input with exactly one output is a function.
Determine whether the relation is a function. Explain.
The following is a relation.
Input Output -1 3 11 5 4
Function; each input has one output

4. Students will be able to determine whether relations are functions.
You try!!
Students will be able to determine whether relations are functions.
Determine whether each relation is a function. Explain.
Each of the following is a relation.
Relation; the input 5 has two outputs
Function; each input has one output
Input, x Output, y
Input, x 2 4 6
Output, y
2.6
5.2
7.8 -2 4
1 2
Function; each input has one output
Relation; the input has three outputs

5. Students will be able to determine whether relations are functions.
We can also use the vertical line test (VLT) to determine if the graph of a relation is a function.
A graph represents a function when no vertical line passes through more than one point on the graph
Function
Passes VLT
Relation
Fails VLT

6. You try!!
Students will be able to determine whether relations are functions.
The following graphs are relations.
Determine whether the graph of the relation is a function. Explain.
Relation; you can draw a vertical line through (2,2) and (2,5)
And (5,1) and (5,5)
Function; no vertical lines can be drawn through more than one point on the graph.
Relation; you can draw vertical lines through two points in several places.
Function; no vertical lines can be drawn through more than one point on the graph.

7. 2. Students will be able to find the domain and range of a function.
Domain: is the set of all possible input values (x-values)
Range: is the set of all possible output values (y-values)
Inputs
Outputs
Write the ordered pairs.
Identify the inputs and outputs.
The domain is -3, -1, 1 and 3.
The range is -2, 0, 2 and 4.

8. 2. Students will be able to find the domain and range of a function.
Domain: is the set of all possible input values (x-values)
Range: is the set of all possible output values (y-values)
Identify the x- and y-values represented by the graph.
y-values
Range
x-values
Domain
The domain is
The range is

9. 2. Students will be able to find the domain and range of a function.
You Try!!
2. Students will be able to find the domain and range of a function.
Domain: is the set of all possible input values (x-values)
Range: is the set of all possible output values (y-values)
Inputs
Outputs
Write the ordered pairs.
Identify the inputs and outputs.
The domain is -2, -1, 0, 1 and 2.
The range is 0, 2 and 4.

10. 2. Students will be able to find the domain and range of a function.
You try!!
2. Students will be able to find the domain and range of a function.
Domain: is the set of all possible input values (x-values)
Range: is the set of all possible output values (y-values)
Identify the x- and y-values represented by the graph.
y-values
Range
x-values
Domain
The domain is
The range is

11. So let’s review!
What have we covered so far?
Students will be able to determine whether relations are functions.
What makes a relation a function?
A relation that pairs each input with exactly one output is a function.
What can we use?
The VLT!
Students will be able to find the domain and range of a function.
What is Domain?
Domain: is the set of all possible input values (x-values)
What is Range?
Range: is the set of all possible output values (y-values)