[Solved] Transformation question

[jaccs]

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

[fun_jirachi]

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

[jaccs]

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]

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!