WEBVTT 00:00:02.790 --> 00:00:04.710 The figure shows the graph of 𝑓 π‘₯. 00:00:05.060 --> 00:00:08.050 A transformation maps 𝑓 π‘₯ to 𝑓 two π‘₯. 00:00:08.350 --> 00:00:11.200 Determine the coordinates of 𝐴 following this transformation. 00:00:11.770 --> 00:00:14.290 As shown here in this question. 00:00:14.350 --> 00:00:19.310 You can see the point 𝐴 is at the coordinates 180, negative one. 00:00:21.030 --> 00:00:27.360 We’re gonna have to see where this 𝐴 moves to when we actually transform our graph to 𝑓 two π‘₯. 00:00:28.750 --> 00:00:32.320 The transformation of 𝑓 two π‘₯ is actually involving stretches. 00:00:32.630 --> 00:00:34.720 I’m gonna have a couple of rules here for stretches. 00:00:36.390 --> 00:00:38.530 The first of these is actually π‘Ž 𝑓 π‘₯. 00:00:38.530 --> 00:00:42.420 And what this is is a stretch by the factor π‘Ž in the 𝑦-axis. 00:00:43.440 --> 00:00:45.100 And what does this actually mean in practice? 00:00:45.260 --> 00:00:49.760 Well what it means in practice is that we’re going to multiply our 𝑦-coordinates by π‘Ž. 00:00:50.180 --> 00:00:50.870 Okay, great! 00:00:50.870 --> 00:00:52.830 So let’s move on to the next stretch. 00:00:54.230 --> 00:01:00.760 Well the next natural rule is that 𝑓 π‘Žπ‘₯ β€” this time you can notice that the π‘Ž is actually inside the parentheses. 00:01:01.360 --> 00:01:05.970 Well this is a stretch by the factor one over π‘Ž in the π‘₯-axis. 00:01:07.210 --> 00:01:08.890 So what does this mean in practice? 00:01:08.890 --> 00:01:18.610 Well what this means in practice is we’re gonna actually multiply our π‘₯- coordinates by one over π‘Ž, which actually is the same as dividing our π‘₯ coordinates by π‘Ž. 00:01:18.830 --> 00:01:19.550 Okay, great! 00:01:19.550 --> 00:01:21.880 So we’ve now got two rules for stretches. 00:01:23.140 --> 00:01:25.490 So now let’s have a look at how we can transform our graph. 00:01:26.900 --> 00:01:38.220 Well actually the transformation that’s gonna be taking place in this question is actually like the bottom one, because we’ve got 𝑓 two π‘₯ so therefore we know it’s going to be a stretch by factor one over π‘Ž in the π‘₯-axis. 00:01:39.600 --> 00:01:44.930 And if we take a look at why that might be the case, well we’ve got 𝑓 two π‘₯ and the two is inside the parentheses. 00:01:45.130 --> 00:01:46.590 So the two is like our π‘Ž. 00:01:48.780 --> 00:01:54.760 So therefore, we actually know it’s gonna be a stretch by the factor one over two or a half in the π‘₯-axis. 00:01:54.760 --> 00:01:56.180 So what does this mean in practice? 00:01:57.280 --> 00:02:00.950 Well what it means in practice is that we’re gonna multiply the π‘₯-coordinates by a half. 00:02:01.200 --> 00:02:01.910 Okay, great! 00:02:02.150 --> 00:02:05.100 So let’s go back to the graph and see if that can help us solve the problem. 00:02:06.440 --> 00:02:09.790 Okay, so what that I’ve actually done is I’ve actually sketched it on our graph in pink. 00:02:11.220 --> 00:02:16.320 Well as you can see, the graph itself actually looks as if it’s been like concertinaed or squashed. 00:02:16.380 --> 00:02:22.550 And that’s actually because what we’ve done is by multiplying our π‘₯-coordinates by half we’ve actually halved each of our π‘₯-coordinates. 00:02:23.830 --> 00:02:36.200 So therefore, if we take a look at what we wanted to find in this question, which is the coordinates of 𝐴, what we can see is that actually I’ve called our new 𝐴 𝐴 dash. 00:02:36.520 --> 00:02:40.300 And the coordinates of our new 𝐴 are 90, negative one. 00:02:40.700 --> 00:02:47.180 And this is because we’ve actually multiplied our 180 by a half because our 180 was our π‘₯-coordinate. 00:02:47.570 --> 00:02:50.510 So multiply 180 by a half, we get 90. 00:02:52.100 --> 00:03:01.300 So therefore, we can say that following the transformation from 𝑓 π‘₯ to 𝑓 two π‘₯, the coordinates of 𝐴 are 90, negative one.