The transformed function will have the same range but may have a different domain.Retain the y-intercepts and coordinates’ positions.When f(x) is compressed horizontally to f(ax), divide the x-coordinates by a.Horizontal compression depends on the scale factor multiplied by the input value (usually x).Summary of horizontal compression definition and propertiesĪre you ready to answer more problems involving horizontal compressions? Why don’t we recap what we learned so far first before we do: The graph shown above confirms this and shows how g(x) is the result of f(x) being horizontally compressed by a scale factor of 4. Let’s go ahead and plot these points and the graph of g(x) to compare the two graphs.Īs we have expected, since g(x)’s input value is scaled by a factor of 4, we expect the graph of f(x) to shrink by the same scale factor. Why don’t we graph the parent function, f(x) = x 2, and plot some reference points as well? Our goal is to graph the function g(x) = (4x) 2.īased on what we’ve just learned, make sure that the coordinate points’ x-coordinates are reduced by 1/4. Make sure that the graph and its points are scaled correctly.Consequently, make sure that the y-intercepts remain in the same position. The y-coordinates would remain in the same position.Make sure to compress the base graph horizontally by checking the reference points’ new positions.Why don’t we start applying our knowledge to compress and graph functions? Before we do, here are some important reminders to remember: We’ve now seen how horizontal compressions affect the graph and points of a function’s graph. If the base function passes through (m, n), the horizontally compressed graph will pass through (m/a, n). What do we expect from the transformed functions’ coordinates? Note that despite being compressed horizontally, the y-coordinates and intercepts remain the same. We also expect a similar effect when x is multiplied by 4, but this time, the graph compresses by a scale factor of 4. Why don’t we compress f(x) = x 2 by scale factors of 2 and 4?Īs can be observed from the graph, when we multiply x by 2, the new graph is a compressed version of the original graph. This means that when we multiply x by a scale factor greater than 1, we expect its graph to shrink by the same scale factor. Given that y = f(x) is the function that we want to transform, f(x) will undergo a horizontal compression when the scale factor, a ( where a > 1), is multiplied to the input value or x for this case. Observe how vertical compressions are applied to graphs here.Īs for this article’s goal, why don’t we go ahead and learn more about horizontal compression? What is a horizontal compression?.Learn how you can vertically and horizontally stretch graphs.Master vertical and horizontal translations.Identify and learn how common parent functions are graphed.Think you need a refresher in any of these topics below? Feel free to click the links! This is why we’ve written about this topic extensively. Isn’t it interesting that by inspecting coefficients, we can either stretch or compress a function’s graph? Mastering the different types of transformations will save us time and help us better understand functions and graphs. Horizontal compressions occur when the function’s base graph is shrunk along the x-axis and, consequent, away from the y-axis. Is it possible for us to shrink or compress graphs horizontally? When do we compress graphs along the x-axis, and how does it affect its expression? These are some of the questions you’ll be able to answer once we learn about this unique transformation technique: horizontal compression. The normal force can be less than the object’s weight if the object is on an incline, as you will see in the next example.Horizontal Compression – Properties, Graph, & Examples (This is not the unit for force N.) The word normal means perpendicular to a surface. If the force supporting a load is perpendicular to the surface of contact between the load and its support, this force is defined to be a normal force and here is given the symbol \(N\). We must conclude that whatever supports a load, be it animate or not, must supply an upward force equal to the weight of the load, as we assumed in a few of the previous examples. Elastic restoring forces in the table grow as it sags until they supply a force \(N\) equal in magnitude and opposite in direction to the weight of the load. (b) The card table sags when the dog food is placed on it, much like a stiff trampoline. \) equal in magnitude and opposite in direction to the weight of the food \(w\).
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