Which function has a range limited to only negative numbers?

When we have a function:

y = f(x)

The possible values of y are the range, and the possible values of x are the domain.

If the graph of our function is completely under the y = 0 line (or under the x-axis) then the range of our function is limited to only negative numbers.

For example, the graph in the image has a negative range, and it seems to be similar to an absolute value function IxI such that:

The sign is changed.

is moved 2 units to the right

is moved 1 unit down.

So this function is:

f(x) = -Ix - 2I - 1