Login

Welcome, Guest. Please login or register.

September 25, 2023, 04:24:39 am

Author Topic: [Solved] Transformation question  (Read 3220 times)  Share 

0 Members and 1 Guest are viewing this topic.

jaccs

  • Adventurer
  • *
  • Posts: 7
  • Respect: 0
[Solved] Transformation question
« on: July 28, 2020, 10:10:56 am »
0
Hello, doing a question from the nesa sample paper and getting answer as B, but the solutions are saying it is A. Not sure if i am doing something wrong or the answers are incorrect. any help appreciated
« Last Edit: July 28, 2020, 11:23:23 am by jaccs »

fun_jirachi

  • MOTM: AUG 18
  • Moderator
  • Part of the furniture
  • *****
  • Posts: 1068
  • All doom and Gloom.
  • Respect: +710
Re: Transformation question
« Reply #1 on: July 28, 2020, 10:54:42 am »
+3
Hey there, welcome to the forums! :)

Consider what happens when you take each transformation in order.
First, we want to dilate horizontally by a factor of 2 ie. we transform \(\sin^{-1}(x-4) \text { to } \sin^{-1}\left(\frac{x-8}{2}\right)\).

Then, we shift the graph right by 1. Note that this actually means we replace \(x\) with \(x-1\), we don't subtract 1 from the entire expression. The latter is especially problematic as in this case, subtracting 1 from the whole expression actually implies that shifting was done prior to dilation - which is not the case It's important to be careful here, and in any other question that involves this.

Hence, we take the transformation from \(\sin^{-1}\left(\frac{x-8}{2}\right) \text{ to } \sin^{-1}\left(\frac{(x-1)-8}{2}\right)\), which gives you the correct answer.

Hope this helps :)
Spoiler
HSC 2018: Mod Hist [88] | 2U Maths [98]
HSC 2019: Physics [92] | Chemistry [93] | English Adv [87] | 3U Maths [98] | 4U Maths [97]
ATAR: 99.05

UCAT: 3310 - VR [740] | DM [890] | QR [880] | AR [800]
Guide Links:
Subject Acceleration (2018)
UCAT Question Compilation/FAQ (2020)
Asking good questions

jaccs

  • Adventurer
  • *
  • Posts: 7
  • Respect: 0
Re: Transformation question
« Reply #2 on: July 28, 2020, 11:22:50 am »
+1
thank you  fun_jirachi
yes, that actually clarifies things enormously and explains why i have been stumbling through these with about 50% accuracy.

i was just dividing the x by 2, not the entire (x - 4) and then after subtracting the 1 was getting and then

thank you so much, that is perfect and so damn obvious now that you have spelled it out in that way!






fun_jirachi

  • MOTM: AUG 18
  • Moderator
  • Part of the furniture
  • *****
  • Posts: 1068
  • All doom and Gloom.
  • Respect: +710
Re: [Solved] Transformation question
« Reply #3 on: July 28, 2020, 11:39:14 am »
+3
Yep, it's definitely really important to remember not to apply any direct transformations to constants and only to the variables inside the function. In this example, we're essentially turning \(\sin^{-1}(x-4)\) into \(\sin^{-1}\left(\frac{x-1}{2}-4\right)\), then rearranging.

Another trick you might want to consider if you're ever in doubt is to sub some easy points in to check you've got things right - this comes especially handy in multiple-choice so you don't have to do any actual computation. An example of a good choice here includes (4, 0) turning into (9, 0) (doubling the distance from the origin and maintaining the sign, then shifting one to the right). A bit more practice will definitely help you push that accuracy up! :)
Spoiler
HSC 2018: Mod Hist [88] | 2U Maths [98]
HSC 2019: Physics [92] | Chemistry [93] | English Adv [87] | 3U Maths [98] | 4U Maths [97]
ATAR: 99.05

UCAT: 3310 - VR [740] | DM [890] | QR [880] | AR [800]
Guide Links:
Subject Acceleration (2018)
UCAT Question Compilation/FAQ (2020)
Asking good questions