An interactive learning ecology for students and parents in my AP Calculus class. This ongoing dialogue is as rich as YOU make it. Visit often and post your comments freely.
I loved this lesson. Isn't it surprising what relationships you find between functions that seem different? I liked all of the problems that you listed and the explanations are really good, but I was wondering about something. In problem 4 you told us that F, G and H behave the same because they have the same derivative. But why are functions F and H the same function?
Here is another question, in #5 you say that the functions in your family are related by a vertical shift. Can you tell me why that is true? Or even could you tell me what the vertical shift would be between two functions in your family?
1 comment:
Dear Ashlynn,
I loved this lesson. Isn't it surprising what relationships you find between functions that seem different? I liked all of the problems that you listed and the explanations are really good, but I was wondering about something. In problem 4 you told us that F, G and H behave the same because they have the same derivative. But why are functions F and H the same function?
Here is another question, in #5 you say that the functions in your family are related by a vertical shift. Can you tell me why that is true? Or even could you tell me what the vertical shift would be between two functions in your family?
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