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. Another transformation that can be applied to a function is a reflection over the x- or 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. functions using reflections about the x-axis and the y-axis. 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. 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 reflection of a point $(x,y)$ over the x-axis will be represented as $(x,-y)$.Īllan was working as an architect engineer on a construction site and he just realized that the function $y = 3x^+4(-x) -1)$.\) In that case, the reflection over the x-axis equation for the given function will be written as $y = -f(x)$, and here you can see that all the values of “$y$” will have an opposite sign as compared to the original function. When we have to reflect a function over the x-axis, the points of the x coordinates will remain the same while we will change the signs of all the coordinates of the y-axis.įor example, suppose we have to reflect the given function $y = f(x)$ around the x-axis. How To Reflect a Function Over the X-axis
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