Final answer:
The domain and range of the function g(x) = x / -4 are both all real numbers, as any real number can be input into the function, and any real number can be the output. None of the provided options accurately represent the range of the function.
Step-by-step explanation:
The question asks us to identify the domain and range of the function g(x) = x / -4. The domain of a function is the set of all possible input values (x-values) for which the function is defined, while the range is the set of all possible output values (y-values).
For the function g(x) = x / -4, we can insert any real number for x, which means the domain is all real numbers. Since multiplying a real number by a negative will also result in a real number and considering that dividing by a constant does not restrict the possible y-values, the range is also all real numbers. However, since we are dividing by a negative number, -4, the result will be the opposite sign of the input x. Therefore, for any positive value of x, g(x) will be negative, and for any negative value of x, g(x) will be positive. This means the range of g(x) is all real numbers without any restriction on being greater or less than -4.
The correct answer is: D = all real numbers & R = all real numbers, which doesn't exactly match any of the options provided. Therefore, the options A, B, C, and D all include incorrect specifications of the range.