Transformations Functions

Can someone please explain how I do questions:

f) i)
f) ii)
h) i)
h) ii)

Thanks for any help

(f) is to do with vertical stretches. Part (i) can be rewritten as $2y=f(x)$ where the transformation is $y \mapsto 2y$ which suggests a vertical stretch by a factor of 1/2. I.e. the graph squishes down towards the x-axis by a distance factor of 1/2.

(h) concerns horizontal transformations. $y=f(\frac{2}{3}x)$ is the transformation $x \mapsto \frac{2}{3}$ which suggests a stretch factor of $\frac{3}{2}$ horizontally away from the y-axis.

Thank you very much! This is really helpful
I know all the questions on the left hand side are on our syllabus and we are expected to learn but do you think we are expected to learn questions f and h at gcse too? Could they be on our exams?

I don't know, I'm not a teacher and sat the old spec 4 years ago.

@Notnek might be more suitable to answer this.

Thank you very much! This is really helpful
I know all the questions on the left hand side are on our syllabus and we are expected to learn but do you think we are expected to learn questions f and h at gcse too? Could they be on our exams?

For 9-1 GCSE maths you only need to know about translations and reflections so that's transformations of the form

f(x + a), f(x) + a, -f(x) and f(-x).

Stretches i.e. f(ax) and af(x) used to be in GCSE but are not anymore. So only a, b, c, d and i are relevant questions. Is this an A Level textbook?

It's worth reading through your spec if you're ever unsure what's included in GCSE.

I don't think you need this for GCSE but it's always good to learn some more e.g. f(ax), af(x), f(x+a), f(x)+a are the standard ones but good to read up on f(ax+b) and dealing with these type of problems. The more you understand it, the more you'll be ready for any question,

Yeah I’m fairly comfortable with all 6 transformations and different variations (like the one you stated). I will check with my teacher what’s in our spec, I only asked to take a photo of those questions because I thought questions f and h were interesting.

My maths teacher went through stretches f(ax) and af(x) and she said we needed to know all 6 transformations. And yes this is from an A-Level textbook.

Alright, good idea, ask your teacher. Are you learning AS Maths right now?

No still working at GCSE

Your maths teacher is incorrect. Many schools still teach stretches at GCSE because they still use old schemes of work or textbooks designed for the old spec. Or they don't realise that stretches aren't in GCSE anymore

I don't know what spec you're doing but for e.g. Edexcel page 14:

A13 sketch translations and reflections of a given function

You'll find a similar thing for all the other exam boards.

For you there's no harm in learning stretches as well because you'll need them for A Level. But you won't ever see them in a GCSE exam.

Ah. Was that a GCSE book?

No it was taken from an A-Level textbook, my teacher can’t get any other resources (probs coz she doesn’t care lol)

Ah. AS book?