Question

In the function f(x) = sec 2x, what are the following:
- Domain
- Asymptotes

Answer 1

Domain will have gaps.

\(f(x)=\sec^2(x)\)

\(f(x)=\displaystyle \frac{1}{ \cos^2(x)}\)

so for every value where cos²(x)=0, you have a vertical asymptote.

Answer 2

Wait, so \[\sec^2x \] is also \[\sec2x\]?

Answer 3

Can I use the T-table to graph the function or nah?

Answer 4

Also, you know that |cos x| < |sec x|
And cos(x) (as well as sine), is between 1 and -1.

This way, |sec x| is always ≥1 and ≤-1.
So, it will look roughly like this: