Chapter 6.5, Problem 4AYU

The graph of $y=\sec x$ is symmetric with respect to the _______ and has vertical asymptotes at _______________.

To determine

To find: The graph of $y=secx$ is symmetric with respect to_____ and has vertical asymptotes at ____.

Answer to Problem 4AYU

Solution:

$y\text{-axis}$; $x=odd multiples of \frac{\pi }{2}$.

Explanation of Solution

Given:

The graph of $y=secx$.

Calculation:

The graph of the function $y=secx$ is,

From the graph we can see that it is symmetric about $y\text{-axis}$.

Moreover, we see that the function goes to infinity for the points.

$x=\pm \frac{n\pi }{2}$, where $n$ is odd integer.

Therefore, the graph of $y=secx$ is symmetric about $y\text{-axis}$ and has vertical asymptotes at $x=\pm \frac{n\pi }{2}\left(i.e\right) x=odd multiples of \frac{\pi }{2}$.