Domain and Range of the Tangent Function

The domain and range of the tangent function is different then the sine and cosine functions.

Analyze the following graph.

y = tan x

The graph of the tangent function covers all of the y-values. This means that the range of the tangent function is All Real Numbers. This will not change no matter the transformation.

We need to pay close attention to the domain. Notice that the graph of the tangent function has asymptotes. For example, there is an asymptote at x = .The domain of the tangent function is All Real Numbers except at x = 90° + n180°, where n is any integer.

For example, if n = 0 then the asymptote occurs at 90°. When n = 1 then the next asymptote occurs at 90° + (1)180° = 270°. This process can continue indefinitely for all integers n.