[Powerprep Plus III Spoiler] Can someone explain this logic to me?

[leenco]

Hi all,

This question confuses me. I thought when we have function and we subtracted 3 from it, the graph should shift downwards, but in the explanation it says that this graph will shift to the right, and therefore the answer is 3.

To shift to the right I thought it would be in the notation of (x-2)^2, where we need to exponent to signal a shift right.

If anyone could explain the difference, it would be greatly appreciated.

[vidishas99]

I like to think of examples for solving such questions:

y = g(x) = x^2 + 1
y2 = g(x+1) = (x+1)^2 + 1

x = -2, -1, 0, 1, 2
y1 = 5, 2, 1, 2, 5
y2 = 2, 1, 2, 5, 10

Adding 1 to the equation shifted it to left; subtracting 5, will shift it to right, leading to no change in the number of roots.

@leenco

I thought when we have function and we subtracted 3 from it, the graph should shift downwards

What you are talking about would be true had this been:
y3 = g(x) -5
In which case:
y3 = 0, -3, -4, -3, 0 (A downward shift)