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.
In this problem, instead of giving the equations of some functions and asking learners to sketch the graphs, this challenge gives the graphs and asks them to find their equations. This encourages learners to experiment by changing the equations systematically to discover the effect on the graphs.
More Parabolic Patterns and Parabolas again offer similar pictures to reproduce. Cubics uses graphs of cubic functions, and Ellipses gives the opportunity to investigate the equation of an ellipse.
Learners could begin by investigating translation of straight lines and look at how the equations change.