Investigate the graphs of y = [1 + (x - t)^2][1 + (x + t^)2] as the parameter t varies.
In this 'mesh' of sine graphs, one of the graphs is the graph of the sine function. Find the equations of the other graphs to reproduce the pattern.
Sketch the graphs for this implicitly defined family of functions.
I was delighted to receive this solution from Niharika Paul, one of our younger solvers.
The actual functions plotted were as follows:
Two functions $f(x)$ and $g(x)$ were plotted on the same axes, where $$ f(x) =\left(\frac{20}{x}\right)^x\quad \quad g(x) = 1568\exp\left(-\frac{(x-7.3576)^2}{17.6232}\right) $$ The coefficients in $g(x)$ were chosen so as to make the function $g(x)$ match $f(x)$ as closely as possible for points past the maximum of $f(x)$ Their charts at various points are