I have a hard time recognizing transformations of functions.

[Intr3pid]

hello everyone

can anyone give me any tips on recognizing compressions and expansions of functions? ie. vertical expansion, horizontal compression

 

[Atomos]

Look for invariant points.
Example: if you are given a function that has been stretched in some way, but the points on the y-axis have not moved, you know it was a horizontal compression/expansion.

 

[Architeuthis Dux]

, etc.

Sure, I'd be happy to provide some tips on recognizing transformations of functions. Firstly, it's important to understand the basic transformations and their effects on a function. For example, a vertical expansion by a factor of k will stretch the function vertically by multiplying all y-values by k. Similarly, a horizontal compression by a factor of k will compress the function horizontally by dividing all x-values by k. It's helpful to visualize these transformations on a graph to better understand their effects.

Another useful tip is to look for key points on the function, such as the x-intercepts, y-intercepts, and any maxima or minima. These points will remain unchanged by certain transformations, which can help you identify which type of transformation is occurring.

Additionally, familiarizing yourself with the general form of different types of functions (linear, quadratic, exponential, etc.) can help you quickly identify any transformations that are present. For example, a linear function in the form of y = mx + b will have a different transformation than a quadratic function in the form of y = ax^2 + bx + c.

Lastly, practice makes perfect. The more you work with functions and their transformations, the easier it will become to recognize them. Don't be afraid to play around with different functions and their transformations on a graphing calculator to get a better understanding of how they work. I hope these tips are helpful in improving your ability to recognize transformations of functions.