Math 1 · Unit 2 · Lesson 4
Reading a Graph: The Behaviors
One checklist that reads any graph, even one with no formula behind it: the intercepts (where it crosses an axis), where it is increasing and decreasing (climbing and falling), where it is positive and negative (above and below the axis), the maximum and minimum (highest and lowest points), and the end behavior (what happens at the far ends).
The big idea
A graph is a picture of a story, and you can read it without any formula. Run the same checklist every time. Intercepts: where it crosses an axis, the output is 0 on the x-axis and the input is 0 on the y-axis. Increasing or decreasing: climbing or falling as you read left to right. Positive or negative: above or below the x-axis, which is a different question from climbing or falling. Maximum and minimum: the highest and lowest points, with where they happen. End behavior: what the far ends do, said plainly first and then with the word infinity. Say where each thing happens with an inequality, and say what it means in the story.
The parts of this lesson
Each part is its own short page. Go in order, or pick the one you need.
Printables
One page with the five-step checklist, the increasing-versus-positive warning, the words we use, and the ball graph read all the way through. Plus a worksheet with an answer key and a short lesson plan.