![]() The student should be able to represent reflections by drawing. The student should be able to state properties of reflections. We also attempted to master the following Tanzania National Standards: Specify a sequence of transformations that will carry a given figure onto another. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. See this in action and understand why it happens. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. 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). R epresent transformations in the plane using, e.g., transparencies and geometry software describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). 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.As we worked our way through this webpage, we attempted to master the underlined parts of the following Common Core State Standards: 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. It's going to be stretchedĪlong the vertical 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. One of the transformations you can make with simple functions is to reflect it across the X-axis. When the light rays from an object get reflected from a. 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 Some of the common examples include the reflection of light, sound, and water waves. 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 Once again, whatever absolute value of x was giving you before for given x, we now wanna get the negative of it. 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 The absolute value of x but now we wanna flip across the x-axis and we wanna get the negative of it. 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 Pads with the reflection of the vector mirrored on the first and last. So for example, if I have some x value right over here, before, I would take Pads with the minimum value of all or part of the vector along each axis. 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. ![]() We can all together visualize what is going on. To draw it visually but I will just so that For each of my examples above, the reflections in either the x- or y-axis produced a graph that was. We really should mention even and odd functions before leaving this topic. What is the equation of the new graph? So pause the video and see Reflection in y-axis (green): f(x) x 3 3x 2 x 2. 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. ![]()
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