Explanation:
f(x) = 5|x - 1| - 5
f(x) will be positive that means >= 0, if
5|x - 1| - 5 >= 0
5|x - 1| >= 5
|x - 1| >= 1
that will be true for x <= 0 or x >= 2
f(x) will be negative for the other cases.
so, 0 < x < 2
f(x) is increasing in
[1, infinity)
the value "1" is for sure included, as it starts the increasing part.
f(x) is decreasing in
(-infinity, 1]
"1" is again included, because it ends the decreasing part.
end behavior means for x going to infinity and -infinity : in both cases f(x) goes to infinity.