maths question help

Can anyone helps with this question please? Not sure what topic this is/ where to even start.

Do you know what the sine graph looks like?

yes but not sure what sort of transformation they want me to do

When sketching graphs, it's often less efficient to think in terms of transformations.
If you know how the sine graph looks like, mark some critical points (i.e. points where you can easily find without much heavy calculations), then "fit" the sine graph onto them.

So... what are some of the critical points? That'd be your job. In fact, the question requires you to do so (i.e. "label the important values on the axes").

yes but not sure what sort of transformation they want me to do

I disagree - what evidence do you have to say that?

From experience. At least it works for me. (In other words, no evidence)
That said, if others find thinking in transformations to be easier, then good for you. No "best method" here as long as you get the job done when it comes to curve sketching, IMO.

I just find it very confusing in the particular case of, say, transforming y=f(x) to y=f(2x). I'd rather just find the easy points, like the zeros/max/min/intercepts, and fit the graph in.

That won't work if they ask for the transformations though ...

Well, sure... But if method is not specified, I don't really care.

So you know what - sine looks like? Then what does the '5' do?

No idea

Can anyone helps with this question please? Not sure what topic this is/ where to even start.

Really? Have you been taught this topic?

All the y values are 5 times bigger ...

well, all you really need to know is what the regular sine graph looks like and what each number represents. (Asin(Bx+C)+D)
-5 here represents the amplitude, and to find the top and bottom critical points, you add/subtract the vertical translation from the amplitude.
+7 represents a vertical translation, meaning you move the entire graph up 7 spaces.
here's a hint, the critical value at 90 degrees is y=2.

Thanks for this response.

So essentially for every point I multiply by -5 and add 7?

Normally on the sine graph the point would be (90,1)
1 x -5 = -5
-5 + 7 = 2
So (90,2)

And I do this for all the main points?

well, all you really need to know is what the regular sine graph looks like and what each number represents. (Asin(Bx+C)+D)
-5 here represents the amplitude, and to find the top and bottom critical points, you add/subtract the vertical translation from the amplitude.
+7 represents a vertical translation, meaning you move the entire graph up 7 spaces.
here's a hint, the critical value at 90 degrees is y=2.

Thanks for this response.

So essentially for every point I multiply by -5 and add 7?

Normally on the sine graph the point would be (90,1)
1 x -5 = -5
-5 + 7 = 2
So (90,2)

And I do this for all the main points?

Not really what s needed ...

If youve done transformations, you should for a standard sin() graph
* -1 multiplier means reflect in the x axis
* 5 multiplier means stretch by 5 (rescale y axis)
* + 7 means vertical translation by 7
Its not wrong to pick points on a standard sin() and multiply by -5 and add 7, but Id guess the question is more about getting you to understand the basic transformations.