Plot the graph of x^y = y^x in the first quadrant and explain its properties.
Investigate the graphs of y = [1 + (x - t)^2][1 + (x + t^)2] as the parameter t varies.
Can you massage the parameters of these curves to make them match as closely as possible?
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.
Here is a pattern composed of the graphs of 14 parabolas. Can you find their equations?
Quadratic graphs are very familiar, but what patterns can you explore with cubics?
Sketch the graphs of y = sin x and y = tan x and some straight lines. Prove some inequalities.
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.
Here is a pattern for you to experiment with using graph drawing software. Find the equations of the graphs in the pattern.