Here is a pattern for you to experiment with using graph drawing
software. Find the equations of the graphs in the pattern.
Here is a pattern composed of the graphs of 14 parabolas. Can you
find their equations?
The illustration shows the graphs of twelve functions. Three of
them have equations y=x^2, x=y^2 and x=-y^2+2. Find the equations
of all the other graphs.
The illustration shows the graphs of fifteen functions. Two of them have equations y=x^2 and y=-(x-4)^2. Find the equations of all the other graphs.
Knowing two of the equations find the equations of the 12 graphs of
cubic functions making this pattern.
Can you massage the parameters of these curves to make them match as closely as possible?
Investigate the graphs of y = [1 + (x - t)^2][1 + (x + t^)2] as the
parameter t varies.
Sketch the graphs of y = sin x and y = tan x and some straight
lines. Prove some inequalities.
Plot the graph of x^y = y^x in the first quadrant and explain its