Vertical and horizontal reflections of a function. In this video you are shown how the function yf (-x) transforms the graph of yf (x) as a reflection across the y-axis. If k k is negative, the graph will shift down. If k k is positive, the graph will shift up. Which of the following describes the transformation of the graph y x2 in graphing y -x2 - 5 reflect over the x-axis and shift down 5 reflect over the y-axis and shift down 5 reflect over the x-axis and shift left 5 See answers Advertisement sqdancefan Let f (x) x². All the output values change by k k units. A vertical reflectionreflects a graph vertically across the x-axis, while a horizontal reflectionreflects a graph horizontally across the y-axis. Given a function f (x) f ( x), a new function g(x) f (x)+k g ( x) f ( x) + k, where k k is a constant, is a vertical shift of the function f (x) f ( x). Transformations are used to change the graph of a parent function into the graph of a more complex function. Another transformation that can be applied to a function is a reflection over the x or y-axis. 11) x y K I H I H K reflection across x 2 12) x y G X F X F G reflection across the y-axis 13) x y N Z X Z X N reflection across x 2 14) x y U B M S M B S U reflection across x 2-2-Create your own worksheets like this one with Infinite Pre-Algebra. Stretching a graph means to make the graph narrower or wider. Write a rule to describe each transformation. They are caused by differing signs between parent and child functions.Ī stretch or compression is a function transformation that makes a graph narrower or wider. Reflections are transformations that result in a "mirror image" of a parent function. Reflecting a graph means to transform the graph in order to produce a "mirror image" of the original graph by flipping it across a line. All other functions of this type are usually compared to the parent function. Sketch the graph of each of the following transformations of y = xĪ stretch or compression is a function transformation that makes a graph narrower or wider, without translating it horizontally or vertically.įunction families are groups of functions with similarities that make them easier to graph when you are familiar with the parent function, the most basic example of the form.Ī parent function is the simplest form of a particular type of function. You should have seen some graph transformations before, such as translations and reflections recall that reflections in the x-axis flip f(x) vertically. Graph each of the following transformations of y=f(x). If a reflection is about the y-axis, then, the points on the right. Graph functions using compressions and stretches. Besides translations, another kind of transformation of function is called reflection. Determine whether a function is even, odd, or neither from its graph. Let y=f(x) be the function defined by the line segment connecting the points (-1, 4) and (2, 5). Graph functions using reflections about the x-axis and the y-axis.
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