Horizontal Compression Linear Examples: A Comprehensive Guide

In this article, we will explore the concept of horizontal compression and its application to linear functions. We will learn how to compress a function by a scale factor and identify vertical compressions given two or more functions' expressions and graphs.

Applying Horizontal Compression to f(x) = 6|x| + 8

Let's apply the concept of horizontal compression to the function f(x) = 6|x| + 8. To do this, we will multiply the function by a scale factor of 1/2. The resulting function is f(x) = 3|x| + 4.

As expected, when the function is compressed horizontally by a scale factor of 1/2, the graph shrinks by the same amount. This means that the x-intercepts of the original and compressed functions are also scaled by the same amount.

Horizontally compressing f(x) by a factor of 1/4 results in the function f(x) = 1.5|x| + 2. Again, we see that the graph shrinks proportionally to the scale factor.

Properties of Horizontal Compression

When a function is horizontally compressed by a rational scale factor, several properties hold true:

* The base of the function's graph remains unchanged.

* The y-intercept of the original and compressed functions are scaled by the same amount as the scale factor.

* If the scale factor is less than 1, the graph will shift to the right. If the scale factor is greater than 1, the graph will shift to the left.

Examples of Horizontal Compression

In addition to compressing linear functions, we can also horizontally stretch or shrink non-linear functions. This technique is useful for modeling real-world scenarios where a function needs to be transformed in order to better fit data.

For instance, if we have a function that models the height of an object at different times, we may want to compress it horizontally to better reflect the actual measurements.

In this article, we explored the concept of horizontal compression and its application to linear functions. We learned how to compress a function by a scale factor and identified vertical compressions given two or more functions' expressions and graphs. By mastering this technique, you will be able to transform functions in a variety of ways to better model real-world phenomena.

Horizontal compression linear examples