Observe symmetries and engage the power of substitution to solve
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.
Here is a pattern composed of the graphs of 14 parabolas. Can you
find their equations?
Knowing two of the equations find the equations of the 12 graphs of
cubic functions making this pattern.
Use functions to create minimalist versions of works of art.
Here is a pattern for you to experiment with using graph drawing
software. Find the equations of the graphs in the pattern.
Prove that the graph of f(x) = x^3 - 6x^2 +9x +1 has rotational
symmetry. Do graphs of all cubics have rotational symmetry?
Draw graphs of the sine and modulus functions and explain the
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.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?