Answer: D
Explanation:
This is a piecewise function. Normally cos x and tan x are continuous functions on their own. but you are using cos x as part and tan x as other part.
In order to see if the function is continuous at 0 plug in 0 for both functions. If it is the same then it is continuous, if different then it is discontinuous. There are no asymptotes in either of the functions so there wouldn't be in any of your answers
2 cos x
2 cos 0 > use unit circle to solve
2 (1)
2
2 + tan x
2 + 0
2
You get the same answer from both functions and one of the symbols is ≥, so the function is continuous.
D is your answer