You say a translation alongside the stretch, but it's worth saying which one is first because the order of performing each transformation matters.
True.
It's either a translation by vector [b,c] followed by a stretch of factor 1/a in the x-direction. Or a stretch of factor 1/a in the x-direction followed by a translation by vector [ab,c]
It's either a translation by vector [b,c] followed by a stretch of factor 1/a in the x-direction. Or a stretch of factor 1/a in the x-direction followed by a translation by vector [ab,c]
Still neither case fits the -1 in her question.
Yeah thats why im confused because it says the phase shift is -1 - unless my teacher made a mistake or phase shift means something else?
Must be a mistake; it's definitely not a minus number, it could be a +1 instead depending on the order of transformation. Phase shift is how much it moves horizontally to the right of the usual position.
So in your case, +1 would make sense for sin(2x−1) if sin(x) was firstly translated by vector [1,0]↦sin(x−1) and then stretched in the x-direction by a factor of 21↦sin(2x−1)
It would be +1/2 if the stretch came first followed by the shift.
Must be a mistake; it's definitely not a minus number, it could be a +1 instead depending on the order of transformation. Phase shift is how much it moves horizontally to the right of the usual position.
So in your case, +1 would make sense for sin(2x−1) if sin(x) was firstly translated by vector [1,0]↦sin(x−1) and then stretched in the x-direction by a factor of 21↦sin(2x−1)
It would be +1/2 if the stretch came first followed by the shift.
So, if the shift came first before the stretch it would be +1?
Unless thats one of the first C3 topics then no i dont think ive learnt that yet?
It should be a C3 topic, one of the early ones too. Besides, that type of question can't just blatantly ask for a horizontal translation without specifying in which order the transformations happen.
How do you go about drawing this sine wave: y=4+3sin(2x-1)
Also i came across a similar question which asks for the phase shift of 5+2sin(2x+1). The answer is 1??
To sketch it, well you know the translations, the stretches, and you can find the stationary points via differentiation which should give you enough info to sketch it. Set yourself a region for it, like between 0 and 2pi which should be enough.
And no, it would be -1 if the translation came before the stretch for that one.