This is a function since it passes the vertical line test. It is impossible to draw a single vertical line to have it pass through more than one point on the curve.
The domain is the set of numbers x such that x is between -3 and +3 excluding those endpoints. In other words, the domain is -3 < x < 3. We never actually get to either endpoint because of the vertical asymptotes.
The range is the set of all real numbers. It is possible to get any output we want depending on the specific input.
To find the sum of a positive and a negative integer, take the absolute value of each integer and then subtract these values. The result takes the sign of the integer with the larger absolute value. The sum of any integer and its opposite is equal to zero.