My question regarding making absolute value fall in a particular range…

My question regarding making absolute value fall in a particular range. In your book you gave two example (pg 149) and my question is what value should I consider as the end? is it the highest value or the (highest value+1) . Because in question#19 pg149 you consideed 181 to be the end, when 181 isn’t included! & what if the inequality symbol is less than or equal to, what should I do in that case?

In the xy plane above, f and g are functions defined by f(x)=abs[x] and g(x)=-abs[x] + 3 for all values x. What is the area of the shaded region bounded by the graphs of the two functions?

Hi mike! This question is from the May 2015 SAT.

(will post photo)

In the xy plane above, f and g are functions defined by f(x)=abs[x] and g(x)=-abs[x] + 3 for all values x. What is the area of the shaded region bounded by the graphs of the two functions?

For all numbers x and y, let x # y be defined by x # y= |x^2-y^2| + 2…

I’m just going to make up a symbol for better visualization. The symbol will look like this: #

For all numbers x and y, let x # y be defined by x # y= |x^2-y^2| + 2. What is the smallest possible value of x # y?

This was a 2/5 on the difficulty scale yet I somehow didn’t understand this and still got it wrong. I tried to do some weird algebra that got me nowhere so I moved on. Funny thing this was the only question I got wrong in the section.

A 0
B 1
C 2
D 3
E 4