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BryceThomas
How do you sketch the function in 1A-2 b) in Problem Set 1?
\[y = \frac{2}{(x - 1)^2}\]
The way I did it was using x= (-3,-2,-1,0,1,2,3) with y = 2/(x-1)². Then you get the coordinates of the function. Notice the vertical asymptote when dividing by 0.
I look at where the function is undefined and what happens when x gets large and negative or when x gets large and positive first: At x=1 there's a division by zero, so there's a big spike there. The expression is always positive (I just noticed this) so the spike goes up. When x is large, either negative or positive, the expression is close to zero. I can now look for where the function crosses the y axis (at 2) and the x axis (not at all?) Later in the course you'll learn other things to look for. If I don't think my graph is good enough at this point, I'll do what MrGonzales suggests to get a clearer picture.
One method is as follows: Plot: \[y = f(x)\] In this case, \[f(x) = 1/x^2\] Now "translate" (move) the function you just plotted using: \[y - y_0 = a\times f(x - x_0)\] You'll find that \[x_0 = 1, y_0 = 0, a=2\]. You'll move the function 1 unit to the right (and zero units up or down). a =2 represents the "zoom out" factor. x0 and y0 represent movement in the x and y axis respectively. This works for all other parts of the problem. Alternatively, you can go to http://www.wolframalpha.com, but that's kinda cheating... :-)