Question

which of the following statements are true about the graph of f(x)= sec x. Select two of the following that apply.

Answer 1

A: (0,1) is a point on the graph.

and

C: There is a vertical asymptote at x = pi/2.

- If you plug in f(x) = sec x into a graphing calculator (i.e. desmos online graphing calculator) you can clearly identify these :)

Explanation:

Answer 2

A. True. Plug in x = 0 and it leads to y = 1.

B. False. The function is undefined when cos(x) = 0 which is when x = n*pi/2 for any odd integer n. So x = pi/2, x = 3pi/2, x = 5pi/2, etc are not allowed as input values.

C. True. This is one of the infinitely many vertical asymptotes, which result from to the fact that x = pi/2 is not allowed in the domain.

D. False. Sine can be equal to zero. The only thing we need to make sure that is nonzero is the cosine value, since secant = 1/cosine

E. False. Choice B talks about values excluded from the domain.

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In summary, the answers are Choice A and Choice C