Martha Richmond

2023-03-19

How to use the graph of $f\left(x\right)=\mathrm{sec}x$ to determine whether the function is even, odd or neither?

shorteghurlxh0m

Beginner2023-03-20Added 10 answers

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

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

A function is even if and only if $f(-x)=f\left(x\right)$, so its graph would be symmetric with respect to the $y$-axis.

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

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

A function is even if and only if $f(-x)=f\left(x\right)$, so its graph would be symmetric with respect to the $y$-axis.

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

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