Grade 12 Loose ends

We have gone over many topics about functions and are heading toward calculation of average and instantaneous rate of change.

We looked at functions and determined with algebra if they are even or odd.

We also looked at inverses to be sure we understood how to calculate them and interpret our answers.

Here’s a sketch of the function and its inverse relation (which is not a function).

And here’s the algebra:swap x and y and isolate y.

When looking for the inverse at 13 we get proof that it is not a function since we get two outputs.

And the inverse at -3 doesn’t exist (no real value), because we cant take square roots of negative numbers, which makes sense when you look at the graph, because there are no points on the graph of the inverse that correspond to x=-3.