![]() Transformations are used to change the graph of a parent function into the graph of a more complex function. ![]() Stretching a graph means to make the graph narrower or wider. Graphic designers and 3D modellers use transformations of graphs to design objects and images. 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. Functions of graphs can be transformed to show shifts and reflections. 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. To reflect the graph of a function h(x) around the y -axis (that is, to mirror the two halves of the graph), multiply the argument of the function by 1 to get h(x). 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). The horizontal reflection produces a new graph that is a mirror image of the base or original graph about the y-axis. See the Transformations Questions by Topic to practice exam-style questions at the basic level.\) We will use point plotting to graph the function. Note that $y$-transformations usually behave as expected as opposed to $x$-transformations that seem to do the opposite. Solution: To graph the function, we will first rewrite the logarithmic equation, y log2(x), in exponential form, 2y x. This does not affect $y$ coordinates but all the $x$ coordinates are flipped across the $y$-axis. Writing graphs as functions in the form (f(x)) is useful when applying translations and reflections to graphs.
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