# which describes how to graph by transforming the parent function

## Graphing by Transforming the Parent Function

Transforming functions is a great way to graph complex and interesting functions without having to break out a pencil and paper to solve lengthy equations. With just a few steps, you can graph and analyze a transformed function using only your computer.

### What is a Parent Function?

A parent function is the simplest form of a function. It cannot be simplified, is not transformed, and represents the most basic equation of a given family of equations. For example, the parent function of linear equations is `y = x`.

### Transformations of the Parent Function

The most common transformations that can be applied to a parent function are horizontal and vertical shifts, stretches, and compressions.

• Horizontal Shift: The function is shifted left or right from its original position. This can be written mathematically as `f(x-a)` where `a` is the number n of places the function is shifted.
• Vertical Shift: The function is shifted up or down from its original position. This can be written mathematically as `f(x) + a` where `a` is the number of places the function is shifted.
• Stretch: The function is stretched along it’s x-axis. This can be written mathematically as `af(x)` where `a` is the scaling factor of the function.
• Compression: The function is compressed along it’s x-axis. This can be written mathematically as `f(ax)` where `a` is the scaling factor of the function.

### Graphing the Transformed Function

Graphing the transformed function is easy with a computer, as most graphing calculators or software can do it quickly.

Open your graphing calculator or software and enter the equation of the transformed function. Then, adjust the window of the graph until you can see the transformed function in full.

You should now be able to see the transformed function, and you can analyze it as desired.

### Conclusion

Transforming functions is a great way to graph and analyze more complex equations without having to do a lot of work. By applying the transformations to the parent function, you can quickly and easily graph any function of your choosing.