Relations that Function
- Author:
- Judah L Schwartz
- Topic:
- Functions
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 supply a value for x, the 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 by sliding the BLACK dot on the horizontal axis.
[integer values for work best]
Choose an operation. The applet will display a curve with the property that every point
on the curve satisfies the relation y <operation> x = .
Can you explain the shape of the curves for the different operations?