New Functions from Old

Guided Notes for this lecture

In mathematics there are often times that multiple functions will involved in models that we create. When we have functions that used within other functions we call these composition functions. We will be reviewing how to create and analyze composition functions.

There are various types of composition functions. We will now look at how we make computations with composition functions.

Just like single functions, composition functions often have restrictions. This next video defines domain and range for composition functions.

While the previous examples looks at creating composition functions, we must also look at the conditions under which composition will not work to understand all the parameters of these types of functions.

Another was in which we create new functions from old functions is by imposting different mathematical operations onto graphs. In this section we will look at the impact of several different mathematical changes to the graph of a function.

Finally, we will look at a few examples of graph transformations.

At the end of this section you should be able to answer the following questions:

1. How do we determine if we can compose two functions? And how do we determine what variable will be used in our final solution?
2. When composing functions, how do we communicate any restrictions on the domain and range?
3. How does the order in which we apply our mathematical operations impact our graphing transformations?

Check Your Understanding
You should try these problems before reviewing the solutions to fill in while watching the video.