WEBVTT
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The figure shows the graph of π π₯.
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A transformation maps π π₯ to π two π₯.
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Determine the coordinates of π΄ following this transformation.
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As shown here in this question.
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You can see the point π΄ is at the coordinates 180, negative one.
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Weβre gonna have to see where this π΄ moves to when we actually transform our graph to π two π₯.
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The transformation of π two π₯ is actually involving stretches.
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Iβm gonna have a couple of rules here for stretches.
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The first of these is actually π π π₯.
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And what this is is a stretch by the factor π in the π¦-axis.
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And what does this actually mean in practice?
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Well what it means in practice is that weβre going to multiply our π¦-coordinates by π.
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Okay, great!
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So letβs move on to the next stretch.
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Well the next natural rule is that π ππ₯ β this time you can notice that the π is actually inside the parentheses.
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Well this is a stretch by the factor one over π in the π₯-axis.
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So what does this mean in practice?
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Well what this means in practice is weβre gonna actually multiply our π₯- coordinates by one over π, which actually is the same as dividing our π₯ coordinates by π.
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Okay, great!
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So weβve now got two rules for stretches.
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So now letβs have a look at how we can transform our graph.
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Well actually the transformation thatβs gonna be taking place in this question is actually like the bottom one, because weβve got π two π₯ so therefore we know itβs going to be a stretch by factor one over π in the π₯-axis.
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And if we take a look at why that might be the case, well weβve got π two π₯ and the two is inside the parentheses.
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So the two is like our π.
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So therefore, we actually know itβs gonna be a stretch by the factor one over two or a half in the π₯-axis.
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So what does this mean in practice?
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Well what it means in practice is that weβre gonna multiply the π₯-coordinates by a half.
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Okay, great!
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So letβs go back to the graph and see if that can help us solve the problem.
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Okay, so what that Iβve actually done is Iβve actually sketched it on our graph in pink.
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Well as you can see, the graph itself actually looks as if itβs been like concertinaed or squashed.
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And thatβs actually because what weβve done is by multiplying our π₯-coordinates by half weβve actually halved each of our π₯-coordinates.
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So therefore, if we take a look at what we wanted to find in this question, which is the coordinates of π΄, what we can see is that actually Iβve called our new π΄ π΄ dash.
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And the coordinates of our new π΄ are 90, negative one.
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And this is because weβve actually multiplied our 180 by a half because our 180 was our π₯-coordinate.
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So multiply 180 by a half, we get 90.
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So therefore, we can say that following the transformation from π π₯ to π two π₯, the coordinates of π΄ are 90, negative one.