The point $x$ is how far to the right of your axis of symmetry? The axis of symmetry has an $x$-coordinate of $-1$, so your distance to the right is $x-(-1)$, or $x+1$. If you're a perceptive sort, you might notice that the sum of each of these pairs of $x$-coordinates is $-2$, and therefore arrive at the transformation rule $x' = -2-x$, but if not, you can still reconstruct what's happening. (KS3, Year 7) The Lesson A shape can be reflectedin the line y x. So in each case, the $y$-coordinate stays the same, but $3$ becomes $-5$, $-2$ becomes $0$, $0$ becomes $-2$, and $13$ becomes $-15$.
The general rule for a reflection over the x-axis: ( A, B) ( A, B) Diagram 3. both coordinates change sign (the coordinate becomes negativeif it is positiveand vice versa). Similar reasoning shows that, for example, A reflection over the x-axis can be seen in the picture below in which point A is reflected to its image A. We will use examples to illustrate important ideas.
X y reflection over y axis how to#
Here, we will learn how to obtain a reflection of a function, both over the x -axis and over the y -axis.
Four units to the left of $x = -1$ is $x = -1-4 = -5$, so the point $(3, -5)$ reflects to $(-5, -5)$. A function can be reflected over the x -axis when we have f ( x) and it can be reflected over the y -axis when we have f (- x ). When you reflect this point, you should end up at the same "height" ($y$-coordinate) of $-5$, but this time four units to the left of your axis of symmetry. (You should follow along and draw things out on a sheet of graph paper or on your computer, in order to make them clear.) Therefore, if you have a point at $(3, -5)$, it is three units to the right of the $y$-axis, but four units to the right of your axis of symmetry. We can understand this concept using the function f (x)x+1 f (x) x +1. A reflection is equivalent to flipping the graph of the function using the axes as references. The reflections of a function are transformations that make the graph of a function reflected over one of the axes. The line $x = -1$ is a vertical line one unit to the left of the $y$-axis. Reflecting a function over the x -axis and y -axis. Rather than think about transformation rules symbolically, and trying to generalize them, try thinking about them visually.
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