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

Aug 3, 2017

$f \left(x\right) = \sec x$ is an even function.

#### Explanation:

The graph of $f \left(x\right) = \sec x$ is shown below:

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

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

If a function is odd, $f \left(- x\right) = - f \left(x\right)$, 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, $f \left(x\right) = \sec x$ is an even function.