Formulae and Graphs

Cartesian and non-Cartesian cars racing.
Check Cartesian Cars!

The positions of the cars depend on the time \(t\). For each car there is a rule for finding the position. The rule is described by a formula in terms of \(t\). Since each value of \(t\) will correspond to one position of a car, the position is a function of the time.

If you want to describe the movement of a car on a paper (where the car cannot move) you can think of \(t\) as changing along one direction and the position along another direction (by using a Cartesian coordinatesystem). Then you can plot the movement. Your plot is the graph of the function.

Find the formula

If you drag \(x_1\), you can see that \(y_1=x_1+2\) for all values of \(x_1\).

Find the formula of the functions \(y_2, y_3, y_4, y_5, y_6\) and \(y_7\).

Use the worksheet below to check your answer, drag \(x\) to see \(y\) move. Enter a formula (in terms of \(x\)) to see another relation. Turn the \(y\)-axis \(90^\circ\) to see the graph of the function.

further info:

Descartes - one of the prohibited authors in Index Librorum Prohibitorum (a list of publications prohibited by the Catholic Church)

by Malin Christersson under a Creative Commons Attribution-Noncommercial-Share Alike 2.5 Sweden License