Q 105 - Precalculus Enhanced with Graphing Utilities

Question

What is the range of the secant function? 

Step-by-Step Solution

Answer

The range of secant function is :-

$(-\infty ,-1]\cup [1,\infty )$.

Step 1. Given Information

We have to find the range of a secant function.

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

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

Step 2. Graph of Secant function

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

Step 3. Analyzing Range

We draw the graph of secant function as following :-

We can see that all the values of $y$ for all values of $x$ are lies from $(-\infty ,-1]$ and $[1,\infty )$.

So we can conclude that range of secant function is $(-\infty ,-1]\cup [1,\infty )$.