How do you use the graph of #f(x)=secx# to determine whether the function is even, odd or neither?

1 Answer
Aug 3, 2017

Answer:

#f(x)=sec x# is an even function.

Explanation:

The graph of #f(x) = sec x# is shown below:

graph{sec x [-10, 10, -5, 5]}

If a function is even, we know that #f(-x)=f(x)#, so its graph would be symmetric with respect to the #y#-axis.

If a function is odd, #f(-x)=-f(x)#, which means that its graph is symmetric with respect to the origin.

In this case, we can see that the graph is symmetric with respect to the #y#-axis. Thus, #f(x)=sec x# is an even function.