What is the Domain Range and Vertical Asymptote of Cotangent

The video tutorial explains how to graph the cotangent function, focusing on its domain and range. It begins by setting up the axes and identifying vertical asymptotes at multiples of π. The domain is defined as all real numbers except where X equals π + πN, where N is an integer. The range is all real numbers, as the graph extends infinitely in both vertical directions. The tutorial emphasizes understanding the behavior of the cotangent function and its repeating pattern.

What is a key characteristic of the cotangent function's graph?

• It is a constant function.

• It has horizontal asymptotes.

• It has vertical asymptotes.

• It is a linear function.

At which points does the cotangent function have vertical asymptotes?

• At every integer multiple of π.

• At every integer multiple of 3π.

• At every integer multiple of π/2.

• At every integer multiple of 2π.

Which of the following describes the domain of the cotangent function?

• All real numbers except integer multiples of π.

• All real numbers except integer multiples of 3π.

• All real numbers except integer multiples of 2π.

• All real numbers except integer multiples of π/2.

What is the range of the cotangent function?

• All positive real numbers.

• All real numbers except zero.

• All negative real numbers.

• All real numbers.

Why does the cotangent function have no vertical constraints?

• Because it is a bounded function.

• Because it extends infinitely in both directions.

• Because it is a periodic function.

• Because it is a linear function.