Question

Choose the function whose graph is given by:

A) y = sec(1/2x) + 2
B) y = 2sec(1/2x)
C) y = 2csc(1/2x)
D) y = 1/2sec(2x)

Answer 1

The graph of the function y = 2sec(1/2x) is represented by option B.

Step-by-step explanation:

The graph of the function y = 2sec(1/2x) is represented by option B.

The secant function is the reciprocal of the cosine function. The parent graph of sec(x) has a period of 2π, while the given function has a period of 4π. This means that the graph of y = sec(1/2x) is compressed horizontally by a factor of 1/2.

The amplitude of the graph is 2, so option B, y = 2sec(1/2x), is the correct function.