![reflection over y axis reflection over y axis](https://showme0-9071.kxcdn.com/files/572396/pictures/thumbs/2017631/last_thumb1431049453.jpg)
If the negative sign belongs to the y, then the graph will flip about the x-axis.
![reflection over y axis reflection over y axis](https://i.ytimg.com/vi/7biZCls8Wh0/maxresdefault.jpg)
Remember Reflections: They appear like opposites Example: y = | –x| will flip the function about the y-axis If the negative sign belongs to the x-value the graph will reflect about the y-axis. In this example, flipping the original function across the y-axis is identical to the original graph (so it looks like nothing happened). Example: y = –|x| will flip the function about the x-axis If the negative sign belongs to the y-value the graph will reflect about the x-axis.ĭo you see how the negative sign is on the inside of the function… affecting the x-value of the function? When you apply a negative to each x-coordinate of each point (-x,y), the graph flips across the y-axis. Examine what happens to make the parent graphs reflect over the y-axis. And then you can see that indeed do they indeed do look like reflections flipped over the X axis.Question: What does a negative do to a graph? Answer: Multiplying a function by a negative sign creates a reflection: y = –f(x) or y = f( –x)įLIPS FUNCTIONS ABOUT THE X-AXIS y = –f(x)ĭo you see how the negative sign is on the outside of the function… affecting the y-value of the function? When you apply a negative to each y-coordinate of each point (x,-y), the graph flips across the x-axis. To reflect an equation over the y-axis, make the x values opposite outside of the symbol. And this bottom part of the quadrilateral gets reflected above it. So you an kind of see this top part of the quadrilateral And what's interesting about this example is that, the original quadrilateral is on top of the X axis. 18 What do you notice about your new coordinates If reflecting over the y axis, the y coordinates will stay the same and the x coordinates will be opposite. We have constructed the reflection of ABCD across the X axis. And we'll keep our XĬoordinate of negative two. Unit below the X axis, we'll be one unit above the X axis.
![reflection over y axis reflection over y axis](https://us-static.z-dn.net/files/d41/4154d78729cfc12f06ad9f4d0be605c3.png)
To find the reflection, we need to cross the y axis which would be x-3. If we reflect across the X axis instead of being one If we look the location of the point on the graph, it is located at x3, y4. Reflections in the y-axis y f ( x ) + a translate up/down by the vector ( 0 a ) y f ( x + a ) translate left/right by the vector ( a 0 ) y. And so let's see, D right now is at negative two comma negative one. When a point is reflected across the x-axis, the x-coordinates remain the same, whereas the y-coordinate changes into its opposite i.e. So this goes to negative five, one, two, three, positive four. So it would have theĬoordinates negative five comma positive four. Units below the X axis, it will be four units above the X axis. The same X coordinate but instead of being four C, right here, has the X coordinate of negative five. The same X coordinate but it's gonna be two I'm having trouble putting the let's see if I move these other characters around. So let's make this right over here A, A prime. So, its image, A prime we could say, would be four units below the X axis. So we're gonna reflect across the X axis. So let's just first reflect point let me move this a littleīit out of the way. Move this whole thing down here so that we can so that we can see what is going on a little bit clearer. The last two easy transformations involve flipping functions upside down (flipping them around the x-axis), and mirroring them in the y-axis. So we can see the entire coordinate axis. And we need to construct a reflection of triangle A, B, C, D. Similarly when we reflect a point (p,q) over the y-axis the y-coordinate stays the same but the x-coordinate changes signs so the image is (-p,q). A vertical reflection reflects a graph vertically across the. Tool here on Khan Academy where we can construct a quadrilateral. Another transformation that can be applied to a function is a reflection over the x- or y-axis. 3) reflection across the x-axis x y F G H 4) reflection across the y-axis x y N M L Find the coordinates of the vertices of each figure after the given transformation. Transformations Homework Packet Intro: Coordinate Plane Label the axes and origin reflection across the x-axis T(2. Rewrite the transformation using reflection notation. Asked to plot the image of quadrilateral ABCD so that's this blue quadrilateral here. y Graph the image of the figure using the transformation given.