Hi Mike …can you solve & explain? (from QAS March 2021)
Section 3; #11.
y = (x-1)(x+1)(x+2)
The graph in the xy plane of the equation above contains the point (a,b). If -1 < or = a < or = 1, which of the following is NOT a possible value of b?
A) -2
B) -1
C) 0
D) 1

First, just in case this is tripping you up, you can substitute a for x and b for y. From there, honestly, I’d just plug in numbers. See what happens when a=-1, a=0, and a=1.

b = (a-1)(a+1)(a+2)

When a=-1, b=(-1-1)(-1+1)(-1+2)=(-2)(0)(1)=0

When a=0, b=(0-1)(0+1)(0+2)=(-1)(1)(2)=-2

When a=1, b=(1-1)(1+1)(1+2)=(0)(2)(3)=0

Because this is a continuous function, if we know it hits -2 and 0 within that range, it must also go through -1. So the answer must be D.

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