Question

Given the graph of $y=\sec 2x.$
Select the correct statements.

Answer 1

Given: $y=\sec 2x$
Now, to find the domain, range and the period of this function, let's use the graph of $\sec 2x$ as shown:

Now, from the graph, $\sec 2x$ is not defined for $x=\cdots \frac{-\pi }{4};\frac{\pi }{4};\frac{3\pi }{4},\frac{5\pi }{4}\cdots$

Hence, every odd multiple of $\frac{\pi }{4}$

$\Rightarrow$ Domain: $R-(2n+1)\pi /4;n\in Z$

Now, from the graph $\sec 2x$ ranges from $(-\infty ,-1]\cup [1,\infty ).$

Or Range of $\sec 2x:R-(-1,1)$

Also, we know the period of $\sec x$ is $2\pi$
Hence, the period of $\sec 2x$ will be $2\pi /2$ or $\pi$