Formulae and Graphs

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.

Non-Cartesian cars.
Change t to let the cars race!

"Cogito ergo sum"

Cartesian cars.
Change t to let the cars race!

Find the formula

Drag the red points!

Find the formula of the functions \(y_i=f(x_i)\) for \(i=1,2,3,4,5\) in the applet above.

Use the applet below to check your answer, turn the y-axis 90° to see the graph of the function.

Drag the red point. Change the slider α to 90°!

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