See how this is applied to solve various problems. We can even reflect it about both axes by graphing y-f (-x). The transformation y af(x) is a vertical stretch of y f(x) with scale factor a parallel to the y-axis and then a reflection in the x-axis. Transformations are used to change the graph of a parent function into the graph of a more complex function. We can reflect the graph of any function f about the x-axis by graphing y-f (x) and we can reflect it about the y-axis by graphing yf (-x). Stretching a graph means to make the graph narrower or wider. A vertical reflection reflects a graph vertically across the x-axis, while a horizontal reflection reflects a graph horizontally across the y-axis. 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. Another transformation that can be applied to a function is a reflection over the x- or y-axis. There are three basic transformations that can be applied to graphs of linear functions: sliding the line around (translation), flipping the line (reflection), and stretching the line. Graphic designers and 3D modellers use transformations of graphs to design objects and images. Reflections are transformations that result in a "mirror image" of a parent function. Functions of graphs can be transformed to show shifts and reflections. Graph functions using compressions and stretches. Describe how the graph of the second function compares to the graph of the first function a) y 3x + 1 y-3x-1 y-(3x+1). Determine whether a function is even, odd, or neither from its graph. 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. Graph functions using reflections about the x-axis and the y-axis. 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. Graph each of the following transformations of y=f(x). Let y=f(x) be the function defined by the line segment connecting the points (-1, 4) and (2, 5).
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