Question

What inequality is graphed?.

y < |x – 2| – 1

y < –|x – 2| – 1

y < |x + 2| – 1

y < –|x + 2| – 1

Answer 1

for big x (positive or negative), |x-2| and |x+2| will be both big. Since the area is below the turned to the negative side, there must be a '-' sign in front of the absolute value.

Answer 2

It's
y < –|x – 2| – 1
or
y < –|x + 2| – 1.

Find among those two the one that has its peak at x=-2. (we see on the graph it's at this point)

Answer 3

is it B?

Answer 4

it's D.

when you look at the graph of f(x) and f(x-a), the one of \(f(x-a)\) is shifted to the right of the quantity \(a\).

|x+2| = |x-(-2)|. <- this one is shifted to the right by a quantity "-2". so it's to the left by quantity 2.

Answer 5

y<-|x+2|-1