{"page":"\u003clink rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/resources-c03aa079.css\" /\u003e\n\u003clink rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/lp_boclips_stylesheets-517835be.css\" media=\"all\" /\u003e\n\u003cdiv data-title='Graph Transformations' data-url='/boclips/videos/634c05cff0c50125a1d070ae' data-video-url='/boclips/videos/634c05cff0c50125a1d070ae' id='bo_player_modal'\u003e\n\u003cdiv class='boclips-resource-page modal-dialog panel-container'\u003e\n\u003cdiv class='react-notifications-root'\u003e\u003c/div\u003e\n\u003cdiv class='rp-header'\u003e\n\u003cdiv class='rp-type'\u003e\n\u003ci aria-hidden='true' class='fai fa-regular fa-circle-play'\u003e\u003c/i\u003e\nVideo\n\u003c/div\u003e\n\u003ch1 class='rp-title' id='video-title'\u003e\nGraph Transformations\n\u003c/h1\u003e\n\u003cdiv class='rp-actions'\u003e\n\u003cdiv class='mr-1'\u003e\n\u003ca class=\"btn btn-success\" data-posthog-event=\"Signup: LP Signup Activity\" data-posthog-location=\"body_link_boclips\" data-remote=\"true\" href=\"/subscription/new\"\u003e\u003cspan\u003e\u003cspan\u003eGet Free Access\u003c/span\u003e\u003cspan class=\"\"\u003e for 10 Days\u003c/span\u003e\u003cspan\u003e!\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv class='rp-body'\u003e\n\u003cdiv class='rp-info'\u003e\n\u003cdiv aria-label='Hide resource details' class='rp-hide-info' role='button' tabindex='0'\u003e\u0026times;\u003c/div\u003e\n\u003ci aria-label='Expand resource details' class='rp-expand-info fai fa-solid fa-up-right-and-down-left-from-center' role='button' tabindex='0'\u003e\u003c/i\u003e\n\u003ci aria-label='Compress resource details' class='rp-compress-info fai fa-solid fa-down-left-and-up-right-to-center' role='button' tabindex='0'\u003e\u003c/i\u003e\n\u003cdiv class='rp-rating'\u003e\n\u003cspan class='resource-pool'\u003e\n\u003cspan class='pool-label'\u003ePublisher:\u003c/span\u003e\n\u003cspan class='pool-name'\u003e\n\u003cspan class='text'\u003e\u003ca data-publisher-id=\"30356647\" href=\"/search?publisher_ids%5B%5D=30356647\"\u003eFuseSchool\u003c/a\u003e\u003c/span\u003e\n\u003c/span\u003e\n\u003c/span\u003e\n\u003c/div\u003e\n\u003cdiv class='rp-description'\u003e\n\u003cspan class='short-description'\u003eGraphs can be shifted and reflected, stretched and squashed. These are all known as transformations. And so now we’re going to look at stretching andsquashing. We will discover how the equation of the graph looks, compared to it’s...\u003c/span\u003e\n\u003cspan class='full-description hide'\u003eGraphs can be shifted and reflected, stretched and squashed. These are all known as transformations. And so now we’re going to look at stretching and\u003cbr/\u003esquashing. We will discover how the equation of the graph looks, compared to it’s changed shape. Let’s start with vertical stretches and squashes as they’re a little easier…\u003cbr/\u003eAs with all vertical transformations, we apply the transformation to the whole function - so the outside.\u003cbr/\u003eVertical Transformations:\u003cbr/\u003eshifts y = f(x) + a the curve up / down\u003cbr/\u003ey = − f(x) reflects the curve in the x-axis\u003cbr/\u003ey = af(x) stretches/squashes the curve vertically\u003cbr/\u003e \u003cbr/\u003eSee how the number goes here...\u003cbr/\u003eSo, because this curve has the equation, y = 2\u003cbr/\u003ex-squared, the 2 means that we need to double\u003cbr/\u003eevery y value...\u003cbr/\u003eSo here, y was at 1 which needs to double to 2\u003cbr/\u003eHere 4 needs to double to 8, So every y-coordinate double in size, If the new curve was y = 3 x-squared, then every y coordinate would need to multiply by 3…\u003cbr/\u003eSo, 1 goes to 3 and so on.\u003cbr/\u003eSee what happens when the equation is y = ½ x-squared... The y coordinates half in size… So, 4 goes to 2. If you have to transform a graph yourself, just take it\u003cbr/\u003epoint by point. So, we have the graph of y = f(x) and we need y = 3 f(x)\u003cbr/\u003eSo, we divide each y-coordinate by 3 Negative 9 moves to negative 3, Negative 6 goes to negative 2, 3 goes to 1. And you’ll end up with your transformed graph… so y = ⅓ f(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 ‘2’ just goes with the x… and ignores the 8. Notice how ‘2’ seems to squash the curve horizontally… whereas ‘½’ stretches the curve... “\u003cbr/\u003eAs with all horizontal transformations they’re a little strange. So, any numbers bigger than 1 will squash the curve, and any numbers smaller than 1 will stretch the curve horizontally.\u003c/span\u003e\n\u003c/div\u003e\n\u003cdiv class='action-container flex justify-between'\u003e\n\u003cbutton aria-expanded='false' aria-label='Read more description' class='rp-full-description' type='button'\u003e\n\u003ci class='fai fa-solid fa-align-left'\u003e\u003c/i\u003e\n\u003cspan id='read_more'\u003eRead More\u003c/span\u003e\n\u003c/button\u003e\n\u003cdiv class='rp-report'\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv aria-labelledby='resource-details-heading' class='rp-info-section'\u003e\n\u003ch2 class='title' id='resource-details-heading'\u003eResource Details\u003c/h2\u003e\n\u003cdiv class='rp-resource-details clearfix'\u003e\n\u003cdiv class='detail'\u003e\n\u003cdl\u003e\n\u003cdt\u003eCurator Rating\u003c/dt\u003e\n\u003cdd\u003e\u003cspan class=\"star-rating\" aria-label=\"4.5 out of 5 stars\" role=\"img\"\u003e\u003ci class=\"fa-solid 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coordinates, x-squared, transformation, curve, horizontally, value, click play, horizontal transformations, curve horizontally, stretches, squashed, number, double, coordinate, graph, stretched, equation, squashes, apply, squared, transform, point, squash, stretch, pause, video, ready, give\u003c/div\u003e\n\u003cdiv class='keyterms-toggle-buttons' data-identifier='Boclips::VideoDecorator634c05cff0c50125a1d070ae'\u003e\n\u003cbutton aria-expanded='false' class='more btn-link' type='button'\u003e\n\u003cspan\u003eShow More\u003c/span\u003e\n\u003ci aria-hidden='true' class='fa-solid fa-caret-down ml5'\u003e\u003c/i\u003e\n\u003c/button\u003e\n\u003cbutton aria-expanded='true' class='less btn-link' style='display: none;' type='button'\u003e\n\u003cspan\u003eShow Less\u003c/span\u003e\n\u003ci aria-hidden='true' class='fa-solid fa-caret-up ml5'\u003e\u003c/i\u003e\n\u003c/button\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv aria-labelledby='classroom-considerations-heading' class='rp-info-section'\u003e\n\u003ch2 class='title' id='classroom-considerations-heading'\u003eClassroom Considerations\u003c/h2\u003e\n\u003cdiv class='classroom-considerations'\u003e\u003cdiv class='fai fa-solid fa-bell'\u003e\u003c/div\u003eBest For: Explaining a topic\u003c/div\u003e\u003cdiv class='classroom-considerations'\u003e\u003cdiv class='fai fa-solid fa-bell'\u003e\u003c/div\u003eVideo is ad-free\u003c/div\u003e \n\u003c/div\u003e\n\u003cdiv aria-labelledby='educator-ratings-heading' class='rp-info-section'\u003e\n\u003ch2 class='title sr-only' id='educator-ratings-heading'\u003eEducator Ratings\u003c/h2\u003e\n\u003cdiv id=\"educator-ratings-root\"\u003e\u003c/div\u003e\u003cdiv id=\"all-educator-ratings-root\"\u003e\u003c/div\u003e\u003cdiv id=\"educator-rating-form-root\"\u003e\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv class='rp-resource'\u003e\n\u003cdiv aria-label='Show resource details' 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rel=\"popover\" tabindex=\"0\" aria-label=\"Play video: Graph Transformations\" href=\"/subscription/new\"\u003e\u003cimg class=\"resource-img img-thumbnail img-responsive z-10 lp-boclips-thumbnail w-full h-full lozad\" alt=\"Graph Transformations\" title=\"Graph Transformations\" onError=\"handleImageNotLoadedError(this)\" data-default-image=\"https://static.lp.lexp.cloud/images/attachment_defaults/resource/large/missing.png\" data-src=\"https://cdnapisec.kaltura.com/p/1776261/thumbnail/entry_id/1_wtp25sj3/width/250\" width=\"315\" height=\"220\" src=\"data:image/png;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs\" /\u003e\n\u003cspan aria-hidden='true' class='flex justify-center items-center bg-white rounded-full w-16 h-16 absolute top-1/2 left-1/2 -mt-8 -ml-8 cursor-pointer z-0 border-2 border-primary drop-shadow-md lp-boclips-thumbnail-playBtn'\u003e\n\u003ci class='fa-solid fa-play text-primary text-3xl ml-1 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