In this lesson you will use geometric transformations to construct a Cartesian graph,named for its inventor, René Descartes and you will analyze how the behavior of a function's variables determines the shape of its graph.
When you finish your construction, be sure to try the Cartesian Games. These games will challenge you while at the same time helping you to deepen your understand of functions.
1 Construct the Graph
Using the tools below, you will dilate `x` on a horizontal number line, rotate the dependent variable to put it on a vertical number line, and translate that result vertically.
You will use the horizontal position of `x` and the vertical position of `T(D(x))` to construct a point with coordinates `(x, T(D(x))).`
By varying `x` and observing the resulting motion of `T(D(x))` you will describe the relative motion of the two variables, and you’ll explain how the relative motion relates to the shape of the traced path of `(x, T(D(x))).`
Use the other pages to construct and compare functions with different values of `s` and `v.`
2 Cartesian Games: Can You Match the Mystery Function?
In this game you control a composed function T∘D (Translation following Dilation) by adjusting the blue dilation scale factor s and the green translation vector v. The challenge is to make your function match mystery function (shown as ??).
3 The Fine Print