### Quartics

Investigate the graphs of y = [1 + (x - t)^2][1 + (x + t^)2] as the parameter t varies.

### Sine Problem

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.

### Cocked Hat

Sketch the graphs for this implicitly defined family of functions.

# Weekly Challenge 43: A Close Match

##### Stage: 5 Challenge Level:

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