For the cotangent function, what is its range?

The cotangent function, defined as the cosine of an angle divided by the sine of that same angle, can take any real number value. This is because as the angle approaches values where the sine is very close to zero (like ( k\pi ), where ( k ) is any integer), the cotangent function will approach either positive or negative infinity. Conversely, at other angles where sine is not zero, cotangent can take on all real numbers in between these extreme values.

Thus, the range of the cotangent function is indeed all real numbers, as there are no restrictions on the values that the function can output. The other options represent ranges that are limited in some way and do not reflect the infinite nature of the outputs that cotangent can produce.