Graph sketching

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

Can you work out which processes are represented by the graphs?

This problem challenges you to find cubic equations which satisfy different conditions.

Find all the solutions to the this equation.

Sketch the members of the family of graphs given by $y = a^3/(x^2+a^2)$ for $a=1, 2$ and $3$.

This function involves absolute values. To find the slope on the slide use different equations to define the function in different parts of its domain.

Can you match these equations to these graphs?

Can you work out the equations of the trig graphs I used to make my pattern?

By sketching a graph of a continuous increasing function, can you prove a useful result about integrals?

Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.