Building blocks

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Reflections

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?

Take a look at the GeoGebra file below. What do you think will happen to the triangles 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 $A$.)

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?