Which of the following statements about the function f (x) = sec(x) are true? select all that apply

First option. f(x) has no zeroes

Second option. f(x) has a period of 2π.

Step-by-step explanation:

1) The function sec(x) is the inverse of the cosine function:

This function has no zeroes, because:

it can not be equal to zero

Then the first option is true.

2) As the secant function is the inverse of the cosine function, it has the same period 2π, then the second option is true.

3) The cosine function has an amplitude of 1, but the secant function does not, then the third option is false.

4) The secant function is symmetric about the y-axis, but not about the origin, then the fourth option is false.

5) The asymptotes of the secant funtion are where the cosine function is equal to zero, this is at integer multiples of π/2, then 5the fifth option is false.  

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step-by-step explanation: