I took the derivative of the given function, found the turning points of that, then determined the turning points.
Okay, so I'm guessing there may a confusion then in how you apply the transformations on a single point. So, what you should've gotten from differentiating is that the turning points of the original function are at:
(0, 0), (9, -2187)
We're translating x in the positive direction by a units, and y in the positive direction by b units. So, this means we're taking on the mapping:
(x', y') --> (x+a, y+b)
Where x' and y' are the images of x and y. So you see, all we need to do to get to those images, is add a and b:
(0+a,0+b), and (9+a,-2187+b)
So, I think the confusion lies in the fact that you probably know to translate an equation in the positive direction, we'd normally do so like this:
f(x-a)+b
The key point here, is that this is for an equation mapping, NOT a point mapping. Here's why:
You can think of our mapping as one in which you have two new equations:
x' = ax+b
y' = cy+d
Now, if I want to put these into the equation y=f(x), I need to solve them for x and y - I can't just substitute x' and y' directly into the equation, because the equation isn't in terms of them - it's in terms of x and y. So, I solve them both:
(x'-b)/a = x
(y'-d)/c = y
I put them into my equation y=f(x):
Which is why for the equations, we minus the translation on x, but for single point mappings, we add the translation on x instead.
Hi!
I was wondering if anyone has a list of irrelevant probability exam questions because I find it hard to tell which questions I should/shouldn't do lol
Thanks~
I don't, sorry, but essentially you can think of it like this - if the probability question looks like something you could answer in year 11, it's probably in the study design still. If it's about binomial distributions or normal distributions, it's in the study design still. If it doesn't fall into one of those three categories, it's probably not in the study design still.