Explanation:
the absolute value function creates only positive functional values. no matter if x is positive or negative.
therefore, the function looks like a big V with the central vertex being at the origin (0, 0).
to reflect this over (or across) to x-axis, we must make sure that now all functional values are negative.
how do we do this ?
we multiply all the positive values of the original function by -1.
f(x) = -|x|
does exactly that.
and to move the function 1 unit to the left, we actually add 1 to the every occurrence of x :
f(x) = -|x + 1|
why ?
because that way the functional value of x+1 happens already for x (and not for x+1). everything happens "earlier".
so, the transformed function is f(x) = -|x + 1|
FYI : for the same reason a subtraction of 1 for every occurrence of x would shift the function to the right (everything happens now later).