What is the domain and range of y = -tan x?

Since the tangent function is an odd function, we'll
re-write the given function as:

-tan x = tan
(-x)

the domain of tangent function is (-pi/2 ; pi/2) or
all real numbers, except pi/2 + kpi, k belongs to Z set of
numbers.

For x = pi/2 + kpi, the tangent function is
undefined.

Let's see why:

The
tangent function is a ratio, where numerator is sine function and denominator is
represented by cosine function:

tan x = sin x/cos
x

If the denominator is zero, then the ratio is undefined.
Since the cosine function is cancelling for x = pi/2 + kpi, then the ratio, namely
tangent function, is undefined.

The range of tangent
function is formed from all real numbers.

f(x) : (-pi/2 ;
pi/2) -> R

f(x) = tan x