Function Transformations
When studying the transformations that can occur in the graph of a function, we have as objective to develop the perception that the knowledge of the graph of a very simple function, will allow us to discover the graphs of other functions, which being of the same type, result from the one of these transformations. This kind of reasoning is so useful that it can be used in the study of more complex functions.
If you want to see these types of transformations occurring in real time, do not hesitate to consult our page about transformations of functions. You can use geogebra to check the changes that occur in the graph of a function when we change small parameters. In the following table you can see a summary of the main transformations that occur in the functions.
| Function | Image | Type of transformation |
|---|---|---|
| `y=f(x)` |  | The original function was created in all graphics with red color and was obtained from the following expression. `f(x) = -0.2 (x + 1) (x - 5) (x - 2)` |
| `y=f(x)+a` |  | Moves it up if `a` is positive or down if `a` is negative. |
| `y=f(x+a)` |  | Moves it left if `a` is positive or right if `a` is negative. |
| `y=af(x)` |  | Stretches or compresses it in the y-direction. |
| `y=f(ax)` |  | Stretches or compresses it in the x-direction. |
| `y=-f(x)` |  | Reflects it about x-axis. |
| `y=f(-x)` |  | Reflects it about y-axis. |
| `y=|f(x)|` |  | The points of zero or positive ordinate remain and the remaining are obtained from the negative ordinate points on a x-axis reflection. |
| `y=f(|x|)` |  | The points of zero or positive abscissa remain and the remaining are obtained from the negative abscissa points on a y-axis reflection. |
If you have any pertinent (math) question and you are not able to easily find a answer, then send us a message through the Contact page. We will be happy to respond. In the event that you detect any errors in our summary tables, do not hesitate to let us know! We will try to correct it as soon as possible.
