## Section8.1Combinations of Functions

¶There are many ways and reasons to combine two or more functions together. In the first exercise, you will combine two functions in the context of performing a familiar activity: paying bills

If you need to add two functions together, such as \(f(x)+g(x)\text{,}\) this represents a combination of functions.

This combination is actually a new function of \(x\text{,}\) whose output is just the sum of the outputs of the functions \(f\) and \(g\text{.}\)

Of course, there are other ways to combine the outputs of two or more functions. In the next exercise, you will practice evaluating other function combinations.

###### Exercise8.1.2

WeBWorK ExerciseAgain, combining functions just means “doing arithmetic” on the outputs of functions. In context, we should be able to describe the meaning of different function combinations.

###### Exercise8.1.3

WeBWorK ExerciseNow we look at the graphs of function combinations. In the next exercise, you will see the effect of multiplying the outputs of two functions to create the combination:

\begin{equation*} y = f(x)g(x) \end{equation*}###### Exercise8.1.4

WeBWorK Exercise###### Exercise8.1.8

WeBWorK ExerciseBy now, you know that all combinations of functions are really just doing arithmetic on the the outputs of the functions. From a graphical standpoint, this just involves combining the \(y\) values of points on the graphs of \(f\) and \(g\text{.}\)

The next problem will have you explore the graph of a particular function combination:

\begin{gather*} f(x) - g(x) \end{gather*}Remember that this is all about combining the outputs of the \(f\) and \(g\) functions.