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#Horizontal compression definition how to

The table of values for f(x) is shown below. We’re now ready to try out more examples and apply our new knowledge on vertical compressions.

When f(x) is compressed vertically, its domain will remain constant, but its range may change.

The value and position of the x-intercept/s are the same.

Apply this concept with the function’s coordinate, so (m, n) becomes (m, an).

When 0 < a < 1, af(x) will return a vertically compressed graph with a scale factor of a.

Here are some important reminders when vertically compressing a given function’s graph or expression: But first, why don’t we recap what we have learned so far before we try other functions and graphs? Summary of vertical compression definition and properties We can apply the same process when vertically compressing other functions. Once we have some of the new compressed graph points, let’s graph the transformed function.įrom this, we can see that when y = 4(x – 4) is compressed by a scale factor of 1/4, the new function is equal to y = x – 4.

The x-intercept (4, 0) will remain the same.

If we want to compress y = 4(x- 4) by a scale factor of 1/4, we’ll have the following points: Why don’t we try compressing y = 4(x- 4) by a scale factor of 1/4?Īs we have mentioned, it’s important to check for reference points and make sure they can get scaled with the right factor.

Retain the x-intercept/s of the graph, but the y-intercept will also decrease by a scale factor of a.

Use critical points and some ordered pairs to guide you in compressing a graph.

Only the values of the y-coordinates will change by a scale factor of a (check if a is a fraction).

Here are some of the important concepts to remember when we transform graphs and compress them vertically: Now, how do we apply this technique when we are given a function’s graph?

#Horizontal compression definition how to

How to vertically compress a function? We’ve now understood how vertical compression affects a base function. Now, what happens with the coordinates of a function that’s compressed by a scale factor of a, where 0 < a < 1? If the base function passes through the point (m, n), the vertically compressed function will pass through the point (m, an).

To compress f(x), we’ll multiply the output value by 1/2. Let’s apply the concept to compress f(x) = 6|x| + 8 by a scale factor of 1/2.

In general, when a function is compressed vertically by a (where 0 < a < 1), the graph shrinks by the same scale factor. Why don’t we observe what happens when f(x) is vertically compressed by a scale factor of 1/2 and 1/4?Īs we may have expected, when f(x) is compressed vertically by a factor of 1/2 and 1/4, the graph is also compressed by the same scale factor. The base of the function’s graph remains the same when a graph is compressed vertically. Vertical compressions occur when a function is multiplied by a rational scale factor. We’ll also apply our knowledge on vertical compressions by graphing different types of functions. This article will show how to identify vertical compressions given two or more functions’ expressions and graphs. Learn how to apply vertical and horizontal stretches as well.Refresh your knowledge of vertical and horizontal transformations.Understanding the common parent functions we might encounter.But by how much? It depends on the scale factor.īefore we start diving deeper into this topic, let’s make sure that we’re equipped with the right techniques and knowledge reviewing the following topics: Vertical compression helps us shrink down functions vertically. Is it possible for us to transform a function by shrinking it down? Yes! One of the most helpful transformation techniques you’ll encounter is vertical compression. Vertical Compression – Properties, Graph, & Examples