# 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.

## 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)