Advanced Integration
📋 What it is
Combine functions with graphs, equations and real data in one rich problem.
🗣️ Coach says
The toughest problems blend it all: read data, fit a function, graph it, then predict. Integration is choosing the right representation at each stage and carrying the rule forward through the whole problem.
🧠 Memory hook
A big problem chains views: data → rule → graph → prediction. Each step feeds the next.
😂 Giggle
What did the domain say to the range?
"I supply the inputs — you show the results!"
😲 Whoa!
Self-driving cars integrate thousands of functions per second — turning sensor data into steering, all in real time.
✅ Quick check: You have data, need a prediction, but no formula yet. What's a strong first step?
Say your answer out loud first — then reveal.
Find the rule from the data (the constant change → the function), then use it to predict.
Deriving the function first unlocks graphing and prediction.
🧪 Try it! (2 minutes)
From data 2,4,6,8 (input 1,2,3,4), find the rule, then predict input 10.