Step-by-step explanation:
just look at the graph and check the typical "special" points.
e.g. when x = 0, and when y = 0, and maybe (depending on the curve) some other interesting ones.
so, what does the graph tell for x = 0 ?
it says y = 5.
that rules out C and D, because they would deliver y = 1/5 for x = 0.
so, it can only be A or B.
now, what does the graph tell us for y = 0 ?
ok, it tells us, x = 1.
that does not help us in this case, as both, A and B deliver y = 0 for x = 1
so, let's look at another good point. good points are points, where we can see pretty precisely their coordinates on the chart, and where these coordinates are even integer numbers.
I see e.g.
x = 2, and y = -5
let's try A
-5 = -5 × cubic root(2 - 1) = -5 × cubic root (1) = -5×1 = -5
so, -5 = -5, that is correct.
let's verify by checking also B
-5 = 5 × cubic root (1 - 2) = 5 × cubic root (-1) = 5×-1 = -5
-5 = -5, again, this is correct.
hmmmmm.
when we think about it, in fact, A and B are the same function (by the way, C and D are equal to each other too).
either your teacher made a mistake or tried to trick you.
A and B are both the right answer.
why ?
A (I only write "cr" for cubic root now)
y = -5 × cr(x - 1) = 5 × -1 × cr(x - 1) = 5 × cr((-1)³(x - 1)) =
= 5 × cr(-1 × (x - 1)) = 5 × cr(x×-1 - 1×-1) = 5 × cr(1 - x) = B
so, A and B are actually equal.
