Final answer:
The range of the given function y = (1/x+2) - 1 is all real numbers except -2.
Step-by-step explanation:
The range of a function represents the set of all possible values that the function can output. To find the range of the given function y = (1/x+2) - 1, we need to determine the possible values of y.
Since the graph of this function is a hyperbola, the range is all real numbers except the value that makes the denominator of the fraction equal to zero.
In this case, the denominator is x + 2, so we can determine the value that makes it equal to zero by solving the equation x + 2 = 0.
The solution is x = -2.
Therefore, the range of the function is all real numbers except -2.