Investigate the graphs of y = [1 + (x - t)^2][1 + (x + t^)2] as the parameter t varies.
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.
Plot the graph of x^y = y^x in the first quadrant and explain its properties.
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.
Can you massage the parameters of these curves to make them match as closely as possible?
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.
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?
Given probabilities of taking paths in a graph from each node, use matrix multiplication to find the probability of going from one vertex to another in 2 stages, or 3, or 4 or even 100.