So I'm doing simultaneous equations with a class in school and we get talking about the sorts of equations that will give 3 sets of solutions. More specifically Equation 1 is a circle and what can equation 2 be so that there are 3 sets of solutions.
We've come up with type 1 where there is a turning point as equation 2 meets to circle
and we've come up with type 2 where you have a graph that double back over itself so that there are only 3 solutions
And I'm sure there's at least a type 3, "where there is a discontinuity in the graph" but I can't come up with an example that works. I know I could manually restrict the domain, but I'm not looking to do that.
Anyone got any ideas?
Here's a great online graphing tool that you could play around with:
https://www.desmos.com/calculator
I'd also be very interested to hear about different types of graphs that give an odd number of intersections