![]() “Private tutoring and its impact on students' academic achievement, formal schooling, and educational inequality in Korea.” Unpublished doctoral thesis. For example, point A' is the image of point A, point B' is the image of point B, and point C' is the image of point C. Tutors, instructors, experts, educators, and other professionals on the platform are independent contractors, who use their own styles, methods, and materials and create their own lesson plans based upon their experience, professional judgment, and the learners with whom they engage. Answer 1 comment ( 28 votes) Upvote Downvote Flag more Ian Pulizzotto 5 years ago In the context of geometric transformations, the prime symbol (') denotes the image of a point as a result of a transformation. Varsity Tutors connects learners with a variety of experts and professionals. Varsity Tutors does not have affiliation with universities mentioned on its website. Media outlet trademarks are owned by the respective media outlets and are not affiliated with Varsity Tutors.Īward-Winning claim based on CBS Local and Houston Press awards. Graph functions using compressions and stretches. Determine whether a function is even, odd, or neither from its graph. Graph functions using reflections about the x-axis and the y-axis. 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.Names of standardized tests are owned by the trademark holders and are not affiliated with Varsity Tutors LLC.Ĥ.9/5.0 Satisfaction Rating based upon cumulative historical session ratings through 12/31/20. Learning Objectives Graph functions using vertical and horizontal shifts. 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. 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 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. ![]() Conceptually, a reflection is basically a 'flip' of a shape over the line of reflection. The negative of that value associated with that corresponding x and so for example, this x, before, we would get Formula, Examples, Practice and Interactive Applet on common types of reflections like x-axis, y-axis and lines: Home Transformations Reflections Reflect a Point Across x axis, y axis and other lines A reflection is a kind of transformation. 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. We can all together visualize what is going on. To draw it visually but I will just so that What is the equation of the new graph? So pause the video and see 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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