Try to complete the following observations about a function that has an inverse.

If the function is increasing, then its inverse is …

If the function is increasing rapidly, then its inverse is …

What assumptions have you made about the function?

*(You may need to click the reset symbol (top right of the graph) to see the triangles and point \(A\).)*

Move point \(A\) to see if the triangles behave as you expect. Do you notice anything else?

Try to complete the following observation about a function that has an inverse.

- If the function or its inverse has a stationary point, then …

Now take a look at this GeoGebra file. What do you think will happen this time if you move point \(A\) along the curve? *(You may need to click the reset symbol (top right of the graph) to see the triangles and point \(A\).)*

What can you now say about the gradients of functions that have inverses?