Question

How do you draw a graph of a relation that is not a function?

Answer 1

There are many answers possible--any graph in two variables is a relation, but only a function if it passes a vertical line test.

We can declare a relation a function if when we draw a vertical line with equation `x = a` on the coordinate plane, with any value of `a`, the line doesn't hit the graph of the function more than once.

So, for instance `y = 2(3)^x`, pictured in the following graph is a function.

graph{2(3)^x [-10, 10, -5, 5]}

However, `(x + 1)^2 + (y - 1)^2 = 1`, pictured in the following graph, is only a relation (not a function).

graph{(x + 1)^2 + (y - 1)^2 = 1 [-10, 10, -5, 5]}

Hopefully this helps!