Graph sketching

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.

Sketch the graph of $xy(x^2 - y^2) = x^2 + y^2$ consisting of four curves and a single point at the origin. Convert to polar form. Describe the symmetries of the graph.

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.

Compares the size of functions f(n) for large values of n.

Explore the rates of growth of the sorts of simple polynomials often used in mathematical modelling.

Explore how can changing the axes for a plot of an equation can lead to different shaped graphs emerging

Several graphs of the sort occurring commonly in biology are given. How many processes can you map to each graph?

How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.

Sketch the graphs for this implicitly defined family of functions.

Plot the graph of x^y = y^x in the first quadrant and explain its properties.