11/6/2023 0 Comments Horizontal compression square root![]() Now that we’ve learned about horizontal stretches and how they affect a base function, it’s time that we apply these on functions’ graphs. What does this mean for the coordinates of the new function’s graph? If the function f(x) passes through (m, n) and is stretched horizontally by a factor of 1/a, the new function will pass through (am, n). When we do this, the output values will remain the same. We also expect all its x-coordinates to increase by 3. Why don’t we compare some values from both functions? x Let’s say we have f(x) = |x|, if this function’s graph is to be stretched horizontally to attain g(x), the new function’s expression can be expressed as |1/3 ∙ x| = |x/3|. Horizontal stretch on other functions will exhibit similar properties. The graph only stretches away from the y-axis when we horizontally stretch a graph. Notice how the y-values remain the same? This is true for all horizontal stretches. Let’s go ahead and look at how f(x) = x 2 will be affected by a scale factor of 1/2 and 1/3.Īs we have expected, the graph stretches by a factor of 2 and 3. What does this mean for functions such as f(x)? When 1/a is multiplied to x, f(x)’s graph stretches horizontally by a scale factor of a. We can apply horizontal stretch to a function by multiplying its input values by a scale factor, a, where 0 < 1/a < 1. These linked articles may help you refresh your knowledge, and when you’re ready, let’s go ahead and learn more about horizontal stretching. Review how we apply vertical stretches.Refresh your knowledge of vertical and horizontal transformations.Understanding the common parent functions we might encounter.Make sure to review your knowledge of parent functions, translations, and vertical stretches before moving to the next section. We can also learn how to speed up graphing new functions based on the scale factors applied. Learning how we can stretch graphs horizontally can help us understand the family of functions’ graphs. ![]() Horizontal stretches happen when a base graph is widened along the x-axis and away from the y-axis. Horizontal stretches are among the most applied transformation techniques when graphing functions, so it’s best to understand its definition. These functions may have been horizontally stretched using a base function. You may already have encountered graphs that look alike but share different widths. Horizontal Stretch -Properties, Graph, & Examples
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