Question

What is the range of the tangent function?

Short answer

The range of tangent function is all real numbers.

Step-by-step solution

Step 1. Given Information

We have to find the range of a tangent function.

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

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

Step 2. Graph of Tangent function  

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

Step 3. Analyzing Range 

We draw the graph of tangent 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 tangent function is all real numbers.