![]() So it's gonna look something, something like that but the key issue and the reason why I'mĭrawing is so you can see that it looks like it'sīeing scaled vertically. Let me make it at least lookĪ little bit more symmetric. It would make it look, it would make it look wider. If we were scaling vertically by something that had anĪbsolute value less than one then it would make the graph less tall. See this in action and understand why it happens. Rule Of Reflections In mathematics, the rule of reflections is a method of solving certain types of problems by reflection. Reflections over the y-axis are called horizontal reflections. Reflections over the x-axis are called vertical reflections. It's going to be stretchedĪlong the vertical axis. We can reflect the graph of yf (x) over the x-axis by graphing y-f (x) and over the y-axis by graphing yf (-x). There are two types of reflections: reflections over the x-axis and reflections over the y-axis. So our graph is now going to look, is now going to look like this. So let's see, two, three,įour, five, six, seven so it'd put it something around that. What this would look like, well, you multiply zero times seven, it doesn't change anything but whatever x this is, this was equal to negative x but now we're gonna get Vertically by a factor of seven but just to understand The negative flips us over the x-axis and then the seven scales What they're asking, what is the equation of the new graph, and so that's what it would be. So I would get y isĮqual to negative seven times the absolute value of x and that's essentially And so if you thinkĪbout that algebraically, well, if I want seven times the y value, I'd have to multiply this thing by seven. You're scaling it vertically by a factor of seven, whatever y value you got for given x, you now wanna get seven times the y value, seven times the y value for a given x. Vertically by a factor of seven and the way I view that is if So that's what reflectingĪcross the x-axis does for us but then they say scaled ![]() If you have a set of coordinates, place a negative sign in front of the value of each y-value, but leave the y-value the same. Practice 1 - Graph the image of P (-6 4) after a reflection over the y-axis. Reflection Over The X-Axis: Sets of Coordinates. Multiple Choices: Transformation The coordinates of a point are given. Once again, whatever absolute value of x was giving you before for given x, we now wanna get the negative of it. Reflection over the x-axis for: Sets of Coordinates (x, y), Functions, Coordinates (with Matrices). Is equal to the negative of the absolute value of x. ![]() In general, if you'reįlipping over the x-axis, you're getting the negative. So in general, what we are doing is we are getting the negative EXAMPLE 2 Test the curve for symmetry, find any x- and y-intercepts and. The absolute value of x but now we wanna flip across the x-axis and we wanna get the negative of it. in part (b) of the preceding example is the reflection through the y-axis of. The negative of that value associated with that corresponding x and so for example, this x, before, we would get The absolute value of x and I would end up there but now we wanna reflect across the x-axis so we wanna essentially get So for example, if I have some x value right over here, before, I would take Now, let's think about theĭifferent transformations. You've seen the graph of y is equal to absolute Sketch so bear with me but hopefully this is familiar. ![]() ![]() It's gonna have a slope of one and then for negative values, when you take the absolute value, you're gonna take the opposite. So for non-negative values of x, y is going to be equal to x. So let's say that's my x-axis and that is my y-axis. Notice that the y-coordinate for both points did not change, but the value of the x-coordinate changed from 5 to -5. We can all together visualize what is going on. For example, when point P with coordinates (5,4) is reflecting across the Y axis and mapped onto point P', the coordinates of P' are (-5,4). To draw it visually but I will just so that What is the equation of the new graph? So pause the video and see \iff \boldsymbol.- The graph of y is equal to absolute value of x is reflected across the x-axis and then scaled verticallyīy a factor of seven. Reflections create mirror images of points, keeping the same distance from the line. Find the expressions of the following reflections of the graph of $y=2x^2-5x+4$, and draw their graphs. We can plot points after reflecting them across a line, like the x-axis or y-axis. ![]()
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