1. Essential Question: How do you use inequalities and interval notation to describe the domain and range of a graph?

2. Inequalities
Equal to – closed circle
Not equal to – open circle

3. Demonstrate where to find the solutions to the inequality on the number line below:
Name some values for x which would make this inequality true:
Number Line:
Why is there an open circle on 5?
Why might it be helpful to plot the inequality on a number line?
5 is not a solution…all of the solutions are greater than 5 but not equal to 5?
Since you cannot list all of the solutions to an inequality using a number line is way to visually see all of the solution to an inequality.

4. Demonstrate where to find the solutions to the inequality on the number line below:
Name some values for x which would make this inequality true:
Number Line:
Why is there a closed circle on -4?
-4 is a solution and should be included in the picture of the numbers in the solutions to the inequality.

5. Compound Inequalities
Compound Inequalities – Two or more inequalities put together.
Name some possible solutions to this inequality:
We know that: and
Try graphing some compound inequalities on number lines with your team!

6. Interval Notation If it’s equal to use brackets [ ]
Essential Question: How do we use inequalities and interval notation to determine domain and ranges of functions and graphs?
Interval Notation
If it’s equal to use brackets [ ]
If it’s not equal to use parentheses ( )
If it’s (infinity) always use parentheses.
Standard: MM1a1 Students will explore and interpret the characteristics of functions using graphs, tables, and simple algebraic techniques.

7. Interval Notation Example: As an interval notation: (5,∞)
Essential Question: How do we use inequalities and interval notation to determine domain and ranges of functions and graphs?
Interval Notation
Example:
As an interval notation: (5,∞)
Note: sets of numbers in interval notation are always read from left to right, as you would move along a number line.
Standard: MM1a1 Students will explore and interpret the characteristics of functions using graphs, tables, and simple algebraic techniques.

8. Let’s Try !!!!! Graph Inequality Interval Notation
Essential Question: How do we use inequalities and interval notation to determine domain and ranges of functions and graphs?
Let’s Try !!!!!
Graph
Inequality
Interval Notation
Standard: MM1a1 Students will explore and interpret the characteristics of functions using graphs, tables, and simple algebraic techniques.

9. Now You Try!!! Graph Inequality Interval Notation
Essential Question: How do we use inequalities and interval notation to determine domain and ranges of functions and graphs?
Now You Try!!!
Graph
Inequality
Interval Notation
Standard: MM1a1 Students will explore and interpret the characteristics of functions using graphs, tables, and simple algebraic techniques.

10. Compound Inequalities/Interval Notations
Essential Question: How do we use inequalities and interval notation to determine domain and ranges of functions and graphs?
Compound Inequalities/Interval Notations
Now, what about numbers greater than 5 but less than 7? Expressed as an inequality this group would look like this:
Make a graph of this inequality on a number line:
Now let’s write it as an interval notation. Remember read the graph from left to right.
Standard: MM1a1 Students will explore and interpret the characteristics of functions using graphs, tables, and simple algebraic techniques.

11. Let’s Try Together!!! Graph Inequality Interval Notation
Essential Question: How do we use inequalities and interval notation to determine domain and ranges of functions and graphs?
Let’s Try Together!!!
Graph
Inequality
Interval Notation
Standard: MM1a1 Students will explore and interpret the characteristics of functions using graphs, tables, and simple algebraic techniques.

12. Now You Try!!! Graph Inequality Interval Notation (-∞,2] U (6,∞)
Essential Question: How do we use inequalities and interval notation to determine domain and ranges of functions and graphs?
Now You Try!!!
Graph
Inequality
Interval Notation
(-∞,2] U (6,∞)
Standard: MM1a1 Students will explore and interpret the characteristics of functions using graphs, tables, and simple algebraic techniques.

13. Day 2: Writing Domain and Range using Inequalities and Interval Notation

14. Example 1:

15. Example 2:

16. Example 3:

17. Example 4:

18. Example 5:

19. Example 6:

20. Example 7:

21. Example 8: