Relations that Function
- Judah L Schwartz
Any curve in the x,y plane is a relation. For example x + y = 5 is the set of values for x and y such that x + y = 5 [(1,4), (0,5), (-2,7) are examples of points that satisfy the relation. The relation x + y = 5 can be written as y = 5 - x. Written this way, we can think of it as a function or recipe. If we supply a value for x, then the function y = 5 - x will produce a value for y. All functions are relations - not all relations are functions! For example, a circle in the x,y plane is a relation, but not a function. Why? This applet allows you to explore four relations that are also functions. Choose a value for the constant alpha by sliding the BLACK dot on the horizontal axis. Choose an operation. The applet will display a curve with the property that every point on the curve satisfies the relation y <operation> x = alpha. Can you explain the shape of the curves for the different operations?