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Core 3 ranges help

I really struggle with ranges (for some reason, I can't get my head around them). Can someone please explain how to answer this question?

f(x) = 3cos(0.5x) for 0 ≤ x ≤ 2pi

I have to find the range of f(x) and I'm not sure what to do. Should I substitute x=2pi and x=0 into f(x)?
Original post by AngryDragon97
I really struggle with ranges (for some reason, I can't get my head around them). Can someone please explain how to answer this question?

f(x) = 3cos(0.5x) for 0 ≤ x ≤ 2pi

I have to find the range of f(x) and I'm not sure what to do. Should I substitute x=2pi and x=0 into f(x)?


For ranges, the things you do are very similar if it involves e, log, or trig functions. If it's any old function like (x^2 - 5x) / 2 then it may be a bit more trickier, but for these ones you just have to think about the functions, how they're different to the functions in the question (eg difference between cosx and cos(0.5x) which doesn't matter for the range) and what other things are going on in the question.

What's the range of values that cos(0.5x) can take? Then think about multiplying that by 3 and what the actual answer is.


Edit: I should add that you should take these things in steps if you can, eg in this case consider cos(0.5x) then 3cos(0.5x), or if f(x) = 5e^(x) - 3 then consider e^x, then 5e^x, then 5e^(x) - 3 etc.
(edited 8 years ago)
Original post by SeanFM
For ranges, the things you do are very similar if it involves e, log, or trig functions. If it's any old function like (x^2 - 5x) / 2 then it may be a bit more trickier, but for these ones you just have to think about the functions, how they're different to the functions in the question (eg difference between cosx and cos(0.5x) which doesn't matter for the range) and what other things are going on in the question.

What's the range of values that cos(0.5x) can take? Then think about multiplying that by 3 and what the actual answer is.


Thank you! It makes a lot more sense now. :smile: I should have thought about that!

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