Combining familiar things can lead to new experiences, sensations, or objects. Adding a motor to a skateboard can lead to new thrills, or medical bills.
Functions may be combined to make new functions. Functions that output numbers can have their outputs combined by arithmetic operations.
The result of such a combination is a new function.
This simulation will allow you to view the graphs of the combinations of several important functions.
Choose a function f of x by selecting one of the nine buttons in the top row of buttons, …
… then choose a second function g of x by selecting one of the nine buttons in the second row.
You can get a look at what the individual functions look like before combining them, if you wish, by using the checkboxes on the left.
When you are ready to see the graph of one of the combined functions, choose which combination you want to see by using the radio buttons.
You can view the graph of neither, either, or both of the uncombined functions at the same time as the graph of the combined function, and you can change which combination is graphed at any time.
Try to predict what different combinations of two functions will look like when graphed before checking yourself. Good luck and good graphing!