The result is that the function [latex]g\left(x\right)[/latex] has been compressed vertically by [latex]\frac{1}{2}[/latex]. Each change has a specific effect that can be seen graphically. The horizontal shift depends on the value of . Conic Sections: Parabola and Focus. Please submit your feedback or enquiries via our Feedback page. This means that most people who have used this product are very satisfied with it. vertical stretching/shrinking changes the $y$-values of points; transformations that affect the $\,y\,$-values are intuitive. Vertical Stretches and Compressions. This type of 3 If a < 0 a < 0, then there will be combination of a vertical stretch or compression with a vertical reflection. What is vertically compressed? You knew you could graph functions. Figure %: The sine curve is stretched vertically when multiplied by a coefficient. If a > 1 a > 1, then the, How to find absolute maximum and minimum on an interval, Linear independence differential equations, Implicit differentiation calculator 3 variables. The graph . I feel like its a lifeline. Consider the graphs of the functions. 2. 5 When do you get a stretch and a compression? When |b| is greater than 1, a horizontal compression occurs. Replace every $\,x\,$ by $\,\frac{x}{k}\,$ to
Step 10. Math can be a difficult subject for many people, but it doesn't have to be! succeed. Much like the case for compression, if a function is transformed by a constant c where 0<11[/latex], the graph is stretched by a factor of [latex]a[/latex]. The general formula is given as well as a few concrete examples. Mathematics. However, with a little bit of practice, anyone can learn to solve them. Copyright 2005, 2022 - OnlineMathLearning.com. a) f ( x) = | x | g ( x) = | 1 2 x | b) f ( x) = x g ( x) = 1 2 x Watch the Step by Step Video Lesson | View the Written Solution #2: Horizontal And Vertical Graph Stretches And Compressions. Let g(x) be a function which represents f(x) after an horizontal stretch by a factor of k. where, k > 1. If [latex]0 1, the graph of y = f (kx) is the graph of f (x) horizontally shrunk (or compressed) by dividing each of its x-coordinates by k. 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