Sept. 21 Class

Learning Goals: Review base functions and inverse functions.

Today we started by reviewing all the base functions and their domain and range.

Linear Function

Quadratic Function

Radical Function

Absolute Value Function

Reciprocal Function

 Cubic Function

 Exponential Function

You should also understand what happens to the domain and range when we transform these functions.


Next we reviewed the inverse of a function.

For a function, , the inverse is denoted .


Example: For the function f(x) = {(1, 2), (3, 2), (4, 5)}, what is the inverse?

Solution: The inverse is found by switching the x and y values,

Notice that this inverse is not a function, even though the original was a function!

The inverse of a function is not always a function.

Example: Find the inverse of f(x) = 3x – 5.

Solution: Follow these steps to find the inverse of an equation,

Example: Find the inverse of this graph.

Solution: You can take each point (x,y) and switch it, then plot the solution, 

OR 

you can reflect the graph over the diagonal line y = x.

Either way, you get this result: