Question

The function $f\left(x\right)=\tan x$ where $x\in (\frac{-\pi }{4},\frac{\pi }{4})$.

• A. is continuous
• B. is discontinuous
• C. is increasing
• D. is decreasing

Answer 1

Answer: (A), (C)

is increasing

Let's try to draw the function in a graph.

Here not that in the domain i.e. $x=\frac{\pi }{2}$ is not present. Domain is $x\in (\frac{-\pi }{4},\frac{\pi }{4})$ for which the function doesn't have any breaks.

Hence in the given interval the function $\tan x$ is continuous or we can say the function is continuous at each and every point in its defined domain.

Also just observation, the function's increasing nature can also be noted.