Reflection around y=x

Turn on function j(x) below (#17), and a point on this function as well (#18)

Now look at that point's reflection around y=x: turn on #20.

Drag the slider below to move the point on our function j, as well as its reflection. Optionally, turn on #23 as well, so better see the "connection" between these two points across y=x.

As you animated these points, what shape do you see the reflected point drawing? Is this what you'd expect?

Now turn on the #28 below to see the reflection of our original function.

You can continue to animate the points above to see how these two relations are reflections of each other

A last question: is our reflection around y=x a function? Answer this, and try to explain two ways in which you know this, in your notes.

Further explorations: Try different functions j(x), by editing #17. You can do this in real time while the reflection is displayed and the points are animating, to explore your results.