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I have the following function

$$f = \sqrt{ 1 + \frac{1}{n}\sum_{t = 1}^T\left(A_t - B_t\right)^2}$$

where $0\leq A_t, B_t \leq 100$ and $A_t \leq A_{t+1}$ and $B_t \leq B_{t+1}$. I am trying to figure out a way to plot this to get an idea for what the surface of $f$ looks like, but I'm not sure how to approach this problem (or if it is even possible). If needed, you can fix the number of values $T$.

John Smith
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  • Which quantities are the variables that you're trying to form a plot from? – Greg Martin Dec 13 '21 at 17:39
  • @GregMartin I'm sort of open to it. Originally I was thinking of it as a 3 dimensional plot with f on the z axis, and A and B on the x and y axis, but it doesn't have to be done that way if something else makes more sense. Alternatively I was thinking maybe a 2D plot could be made where the y-axis is f, and the x-axis is $\sum_t^T(A_t-B_t)^2$. – John Smith Dec 13 '21 at 17:45
  • If it's a 2D plot as you describe in the last sentence, then it's simply the graph of $f(u) = \sqrt{1+\frac1nu}$. – Greg Martin Dec 13 '21 at 17:47
  • @GregMartin, agreed, but how do I calculate u in a meaningful way, or how do I defined the sequence U for plotting? Is $0 \leq u \leq 10000$? – John Smith Dec 13 '21 at 17:49

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