Answer:
All real values less than or equal to -2 or (infinity, -2].
Step-by-step explanation:
The range of the function is the range of what the output can be. Let’s analyze the equation in parts.
Notice that |x-1| must always be greater than or equal to 0, so we know that 1/3|x-1| also must always be greater than or equal to 1/3*0 = 0.
With the negative, however, -1/3|x-1| must be less than or equal to -1/3*0 = 0.
Finally, we take the -2 into account. -1/3|x-1| - 2 must always be less than or equal to 0-2 = -2.
Therefore, the range is all real values less than or equal to -2, which can be written as (infinity, -2].
I hope this helps!
