Question

How do you sketch the function in 1A-2 b) in Problem Set 1?

Answer 1

\[y = \frac{2}{(x - 1)^2}\]

Answer 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.

Answer 3

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.

Answer 4

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... :-)