Question

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

Answer 1

`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.