Reflection Quick Practice - MathBitsNotebookGeo

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There are four types of transformations of functions or graphs Reflection, Rotation, Translation and Dilation. In this guide, we will study the reflections of the function along with numerical examples so that you can grasp the concept quickly. For example, we will write the reflection of a point 3,4 as 4,3.

Reflection over the y-axis. A reflection in the y-axis can be seen in diagram 4, in which A is reflected to its image A'. The general rule for a reflection over the y-axis r_y-axis 9292 A,B 92rightarrow -A, B

Another transformation that can be applied to a function is a reflection over the x- or y-axis. A vertical reflection reflects a graph vertically across the x-axis, while a horizontal reflection reflects a graph horizontally across the y-axis. The reflections are shown in Figure 3-9. Figure 3-9 Vertical and horizontal reflections of a function.

Graphs of Reflections. In geometry, a transformation is an operation that moves, flips, or changes a shape to create a new shape. A reflection is an example of a transformation that takes a shape called the preimage and flips it across a line called the line of reflection to create a new shape called the image.

Another transformation that can be applied to a function is a reflection over the latexxlatex- or latexylatex-axis. A vertical reflection reflects a graph vertically across the latexxlatex-axis, while a horizontal reflection reflects a graph horizontally across the latexylatex-axis. The reflections are shown in Figure 9.

To reflect the graph of a function hx around the y-axis that is, to mirror the two halves of the graph, multiply the argument of the function by 1 to get hx. What is an example of function reflection? To see how function reflection works, let's take a look at the graph of hx x 2 2x 3. The graph of the original function

Example 1. Fig. 1 is the graph of this parabola fx x 2 2x 3 x 1x 3. The roots 1, 3 are the x-intercepts. Fig. 2 is its reflection about the x-axis. Every point that was above the x-axis gets reflected to below the x-axis. And every point below the x-axis gets reflected above the x-axis.

Example 4 Reflections and Shifts Compare the graph of each function with the graph of a. b. c.g x x h x x k x x 2 f x x. Algebraic Solution a. Relative to the graph of the graph of is a reflection in the -axis because b. The graph of is a reflection of the graph of in the -axis because c. From the equation you can conclude that the graph of is

How does a reflection affect the equation of the graph? When a graph is reflected, you can change its equation algebraically . There is no need to sketch the graph. Reflecting in the -axis puts a in front of the whole equation. For example, becomes . This simplifies to . Reflecting in the -axis replaces any with in the equation. For example

Reflection Graph Example 8 As expected, this method also works for functions. Previously, the graph of eqy92sqrt x eq was used. Here is the table with selected points. Notice that additional