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

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Answer 1 · 2017-08-03T01:56:08

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

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.

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