 Graphs can be shifted and reflected, stretched and squashed. These are all known as transformations. We looked at translating and reflecting in these videos. So now we're going to look at stretching and squashing. We'll discover how the equation of the graph looks compared to its chain shape. Let's start with vertical stretches and squashes as they're a little easier. As with all vertical transformations, we apply the transformation to the whole function, so the outside. See how the number goes here? If it's a two, a three, or any number bigger than one, the curve will be stretched. So because this curve has the equation y equals two x squared, the two means that we need to double every y value. Here, four needs to double to eight, so every y coordinate doubles in size. If the new curve was y equals three x squared, then every y coordinate would need to multiply by three. So one goes to three, and so on. See what happens when the equation is y equals a half x squared? The y coordinates half in size, so four goes to two. If you have to transform a graph yourself, just take it point by point. So we have the graph of y equals f of x, and we need y equals a third f of x. So we divide each y coordinate by three. Negative nine moves to negative three, negative six goes to negative two, three goes to one, and you'll end up with your transformed graph. So y equals a third f of x would be squashed vertically by a third. Horizontal stretches and squashes aren't much different. As with all horizontal transformations, we apply the transformation directly to the x's. See how the two just goes with the x and ignores the eight. Notice how two seems to squash the curve horizontally, whereas a half stretches the curve. As with all horizontal transformations, they're a little strange. So any numbers bigger than one will squash the curve, and any numbers smaller than one will stretch the curve horizontally. Here are a couple of questions for you to do. Pause the video, work out the stretches and squashes, and click play when you're ready. Did you get them right? Here's a brain teaser to finish with. It could be any combination of translations, reflections, stretches and squashes. Pause the video, give it a go, click play when you're ready. Did you get six too? If you did, amazing, well done. You must really understand transformations. If you liked the video, give it a thumbs up, and don't forget to subscribe, comment below if you have any questions. Why not check out our Fuse school app as well? Until next time.