What is the Domain Range and Vertical Asymptote of Tangent

The video tutorial explains how to evaluate the domain and range of the tangent function. It begins with a rough sketch of the tangent graph, highlighting its cyclical nature and key features such as intercepts and asymptotes. The domain is identified as all real numbers except where vertical asymptotes occur, which are spaced π units apart. The range is described as all real numbers, as the graph extends infinitely in both positive and negative directions.

What are the initial asymptotes of the tangent function?

• -π/2 and π/2

• 0 and π

• -π and π

• π/4 and 3π/4

How is the domain of the tangent function expressed?

• All real numbers except multiples of π/4

• All real numbers except even multiples of π

• All real numbers except odd multiples of π/2

• All real numbers except multiples of π

What is the distance between consecutive asymptotes in the tangent function?

• π/2

• π

• 2π

• 3π/2

What is the range of the tangent function?

• Between -1 and 1

• Only negative numbers

• All real numbers

• Only positive numbers

Why does the tangent function have no constraints on its range?

• Because it is periodic

• Because it has a finite number of intercepts

• Because it is undefined at certain points

• Because it extends infinitely in both directions