Lesson 3.2
Writing Inequalities from Graphs
Algebra is a two-way street. You learned to draw the picture from the math; now you must learn to write the math from the picture.
Introduction
If you see a speed limit sign, you see a number (65). But your brain translates that image into a mathematical rule: "My speed must be less than or equal to 65." Today, we make that translation explicit.
Past Knowledge
Graphing inequalities on a number line (Lesson 3.1).
Today's Goal
Write the inequality () that matches a given graph.
Future Success
Essential for "Domain and Range" where you read intervals from a graph.
Key Concepts
The 3-Step Scan
Find the Boundary
Where does the shading start? That is your number.
Check the Circle
- Open: No bar ()
- Closed: Add bar ()
Check Direction
- Right: Greater ()
- Left: Less ()
Worked Examples
Example 1: Identify the Inequality
BasicWrite the inequality shown below:
Analyze Features
- Boundary: -2
- Circle: Open (Strict inequality)
- Direction: Right (Greater than)
Write It
Example 2: Left and Inclusive
IntermediateWrite the inequality shown graph:
Analyze Features
- Boundary: 4
- Circle: Closed (Includes "or equal to")
- Direction: Left (Less than)
Write It
Example 3: Analyzing from Zero
AdvancedWrite the inequality shown graph:
Analyze Features
- Boundary: 0
- Circle: Closed ( or )
- Direction: Right (Greater)
Write It
This represents "non-negative" numbers.
Common Pitfalls
Seeing What's Not There
Don't add the "equals" bar just because it looks nice. If the circle is OPEN, the bar MUST be missing. , not .
Direction Confusion
Always write the variable FIRST (). If you write , the arrow direction no longer matches the inequality symbol.
Real-Life Applications
Digital Sensors: A thermostat reads the temperature graph over time. If the graph goes above the "red line" (), it triggers the AC. Writing the code requires translating that visual threshold into an inequality.
Practice Quiz
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