Q 104 - Precalculus Enhanced with Graphing Utilities

Question

What is the range of the cotangent function? 

Step-by-Step Solution

Answer

The range of cotangent function is all real numbers. 

Step 1. Given Information

We have to find the range of a cotangent function.

The range of a function is the set of its possible output values.

We will draw a graph of cotangent function using graphing utility, then calculate its range.  

Step 2. Graph of Cotangent function

By using graphing utility we can draw the graph of cotangent function as following  :- 

Step 3. Analyzing Range

We draw the graph of cotangent function as following :-  

We can see that all the values of $y$ for all values of $x$ are lies all over the real line.

So we can conclude that range of cotangent function is all real numbers.