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

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

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.

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.

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!

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.

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.

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.

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.

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.

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.

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.

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

Example 1:

Example 2:

Example 3:

Example 4:

Example 5:

Example 6:

Example 7:

Example 8: