One variable controlling one variable: a linear example.
Here is a dynamic transformation figure visualizing the functionx -> ax+ b.
To change the values of a and b, drag the arrow points.
To change the value of x, move the point labeled x on its axis.
To change the scale of the figure move the the point labeled 1 on its axis.
Turn the animation on and/or off by clicking on the "animate x" button.
You can slow down or speed  up the animation by using the < and > keys.
See what you can discover about this type of function using this figure.