Question

What are the domain and range of y = cot x? Select onechoice for domain and one for range.

Answer 1

The correct choices are:

A. Domain

D. Range: All real numbers

The function y=cotx represents the cotangent function, which has a domain where the function is defined and a range which comprises all possible output values.

The cotangent function's domain consists of values where its denominator (sinx) is not equal to zero because division by zero is undefined. So, the domain of y=cotx is all real numbers except where

sinx=0. This occurs at integer multiples of π (i.e.,

x=nπ where

n is an integer).

Therefore, the correct choice for the domain of y=cotx is A. Domain:

x=nπ where

n is an integer.

Now, the range of the cotangent function y=cotx is all real numbers except y=0. This means the range of y=cotx is not limited between -1 and 1, as shown in choice B.

Hence, the correct choice for the range of y=cotx is D. Range: All real numbers, excluding y=0.

Answer 2

A. Domain: x ≠ n

D. Range: All real numbers

Explanation:

We have the following function:

`y=\cot\left(x\right)`

The domain of a function is the interval of input values, that is, the interval of x while the range is the interval of output values, that is, the interval of y.

In the cotangent function, x cannot take the value of radians (nor its multiples), since it is not defined, while the range is continuous on all real numbers.

That means the correct options are:

A. Domain: x ≠ n

D. Range: All real numbers