Prove that the graph of f(x) = x^3 - 6x^2 +9x +1 has rotational
symmetry. Do graphs of all cubics have rotational symmetry?
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.
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
$y = x^2$
$y = - (x - 4)^2$
Use a graphic calculator or a graph drawing computer program to sketch these two graphs and then locate them in this illustration. Use the clues given in this information to help you to find the equations of all the other graphs and to draw the pattern of the 15 graphs for yourself. For your solution send in the equations you have found with an explanation of how you did it.
What about the equations of these parabolas?
You may like to use your creative talents to devise your own pattern of graphs and send them to us so that we can base another challenge like this one on the website using your pattern.