We're looking at c = 2 and *f*(*c*) = *f*(2) = 4. We want this point to be in the center of the window, start by graphing *f* with 0 ≤ *x* ≤ 4 0 ≤ *y* ≤ 8. We see this: We want to have *f*(*x*) within 0.1 of *f*(*c*). Therefore we want to have *f*(*x*) within 0.1 of *4*, or 3.9 ≤ *f*(*x*) ≤ 4.1. Change the values of *y* in the calculator window accordingly, to make this picture: Yes, it looks crazy. That means we'll need to restrict *x* a lot. Start with letting *x* only move 0.1 away from 2, so 1.9 ≤ *x* ≤ 2.1, and the picture looks like this: PICTURE: graph that Since we don't have a picture yet, try some other numbers. Having 1.95 ≤ *x* ≤ 2.05 doesn't work, and neither does 1.97 ≤ *x* ≤ 2.03. However, 1.98 ≤ *x* ≤ 2.02 does work, as does 1.99 ≤ *x* ≤ 2.01. Our final answer could be either of these. We could say "restrict *x* to within 0.02 of 2" or "restrict *x* to within 0.01 of 2," and either of these answers would be right. There are other right answers, also. As long as the point (c,*f*(c)) is in the center of the graph, the *y* values are what we want, and the graph shows a curve exiting on the sides of the graph (meaning that we can see what *f*(*x*) is doing for all values of *x* in the window), we have a picture and we've restricted *x* appropriately. |