Lesson 2.2 - Identifying Domain and Range
Learning Objective(s): SWBAT:
1. Identify the domain/range of a given graph and quantify it using
> Inequality Notation
> Interval Notation
How to Identify domain and range:
1. Always define domain/range from the lowest value to the highest value
2. For domain, ask yourself "what are the highest/lowest x values that I see on the graph?"
These are the "boundaries" of the domain (note, it is possible that there is no boundary)
3. For range, ask yourself "what are the highest/lowest y values that I see on the graph?"
These are the boundaries of the range (as with domain, it is possible that there is no
boundary...see #4 below)
4. Notice "end behavior" (where the graph ends both horizontally and vertically). Does the
graph have an arrow going to either positive or negative infinity or are there end points?
5. If the graph has a value for every possible x coordinate, the domain is all real #'s
6. If the graph has a value for every possible y coordinate, the range is all real #'s
• Inequality Notation
> As with any inequality, closed circles mean the end point IS included as a solution.
Use ≤ or ≥ when identifying domain and range
> Open circles mean the endpoint is NOT included as a solution. Use < or >.
Examples: Identify the domain and range of the following function using inequality
notation
-∞ ≤ x ≤ 5
-∞ ≤ y ≤ 2
-5 < x < -2
-4 < y < 4
-4 < x ≤ ∞
-1 < y ≤ ∞
Your Turn: Identify the domain and range of the following function using inequality
notation
Lesson 2.2 - Identifying Domain and Range
Practice: Identify the domain and range for each graph
Bonus: Which three graphs above are NOT functions (and why)?
Lesson 2.2 - Identifying Domain and Range
• Interval Notation: Its all about the continuity of the graph
Continuous Function Example:
Non - Continuous Function Examples:
Not Continuous
(discrete)
> Continuity affects the way we write about (or describe) the Domain and Range of a
function
> If the domain and range are a specific set of non-continuous (discrete) points, use SET
NOTATION
– Example: The domain and range of the function containing the specific points (-1, 2),
(3, 4), (0, 0) and (6, -3) would be written using set notation:
d = {-1, 3, 0, 6}, r = {2, 4, 0, -3}
Your Turn: Use set notation to define the domain and range of the following relation:
(-3,-1), (-2, 4), (-1, 2), (1, -1), (3, -1)
> If the domain and range contain specific sets of continuous points, we use INTERVAL
NOTATION
> When using interval notation, you are, in essence, listing the boundaries of each interval
(segment) of the function.
Lesson 2.2 - Identifying Domain and Range
Examples: Identify the domain and range of the following function using interval notation
(- ∞, 5]
(- ∞, 2]
[- 5, -2]
[- 4, 4]
[- 4, ∞)
[- 1, ∞)
Your Turn: Identify the domain and range of the following function using interval notation
Lesson 2.2 - Identifying Domain and Range
Practice
Use Interval Notation
Use Interval Notation
Lesson 2.2 - Identifying Domain and Range
Practice
Use Interval Notation
Use Interval Notation