let takes x=1 , z_2 = 1 \cdot 2 - 4 \implies a_2 = 0, the line would roughly be

Now here comes the doubt, the black dotted line works fine where cutoff happens a t x=1, but in the red dotted line the cutoff at x=2 gives us y =1, it is not setting it to 0. Am i missing something?

Just to confirm, the first layer will divide data like this

The above graph is the result of a(x) = a_0(x) + a_1(x) + a_2(x), so you need to consider all three of them for every x. Give it a try and you should get consistent answers with the graph!

is a^{[2]} = \sum_{i=0}^2 a^{[i]} mean composition of function? According to me yes, because it is taking some functions and returning another function?

If I expand the summation sign in this equation from you:

This is what I will get: a^{[2]} = a^{[0]} + a^{[1]} + a^{[2]}, do you agree? If so, I notice that the subject in the left hand side appears in the third term of the right hand side. Therefore, I do not understand this equation.

Would you mind to rephrase your question but using the symbols defined in this screenshot, if we are still discussing this I assume? If so, this can save your time defining the meaning of each symbol you use in your question.

They wonâ€™t look similar because the following graph

has an x-axis scaled from 0 to 3 and y-axis from 0 to 4, but yours is totally different.

I found that the lab uses this np.linspace(0, 3, 3*100) to initialize X. To reproduce the labâ€™s result, it is easier if sticking with the labâ€™s setting. The labâ€™s notebook doesnâ€™t show a lot of source code, but you might always click â€śFileâ€ť > â€śOpenâ€ť (on the menu bar of the notebook) to browse and open the source code which is imported by the lab.