Question

Which statements are true about the graph of f(x)=cot(x)? Select each correct answer. Responses The graph will have a vertical asymptote at x=π2. The graph will have a vertical asymptote at , x equals pi over 2, . The graph will have a vertical asymptote at x=π. The graph will have a vertical asymptote at , x equals pi, . The graph will have a vertical asymptote at x=3π2. The graph will have a vertical asymptote at , x equals fraction numerator 3 pi over denominator 2 end fraction, . The graph will have a vertical asymptote at x=2π. The graph will have a vertical asymptote at , x equals 2 pi, . The graph will go through the point (π4, 1). The graph will go through the point , left parenthesis pi over 4 comma 1 right parenthesis, .

Answer 1

Explanation:

Answer 2

the correct responses are:

The graph will have a vertical asymptote at x = π/2.

The graph will have a vertical asymptote at x = 3π/2.

The graph will have a vertical asymptote at x = 2π.

The graph will not go through the point (π/4, 1).

Explanation:

The statements that are true about the graph of f(x) = cot(x) are:

The graph will have a vertical asymptote at x = π/2.

The graph will have a vertical asymptote at x = 3π/2.

The graph will have a vertical asymptote at x = 2π.

These are true because the cotangent function has vertical asymptotes at every odd multiple of π/2, which includes π/2, 3π/2, and 5π/2, and so on.

The statement that the graph will go through the point (π/4, 1) is false. The cotangent function does not pass through this point, although it does have a vertical asymptote at x = π/4.

Therefore, the correct responses are:

The graph will have a vertical asymptote at x = π/2.

The graph will have a vertical asymptote at x = 3π/2.

The graph will have a vertical asymptote at x = 2π.

The graph will not go through the point (π/4, 1).