Advanced Synthesis
📋 What it is
The capstone: model, graph, analyse and predict with functions end to end.
🗣️ Coach says
Everything comes together: read a situation, build its function, graph it, analyse its behaviour, and predict. Synthesis is running that whole chain smoothly and choosing the right tool at each step.
🧠 Memory hook
Model → graph → analyse → predict. One rule carried cleanly through every stage.
😂 Giggle
What did the exponential function say at the gym?
"I just keep growing — faster and faster!"
😲 Whoa!
Predicting a rocket's path chains functions for thrust, gravity and drag — synthesis at the highest level.
✅ Quick check: A synthesis task gives real data and asks for a week-10 prediction. Outline the plan.
Say your answer out loud first — then reveal.
Find the rule from the data, write the function, (optionally graph it), then evaluate it at input 10.
Synthesis links deriving, representing and evaluating a function.
🧪 Try it! (2 minutes)
Take savings data (5,10,15,20), find the rule, graph it, and predict week 8.