Below is a graph of the function $y=\(\sec\[\left\)(bx-\(\pi\]\right\))$. Determine the value of b.

• A. $b=2$
• B. $b=4$
• C. $b=\(\frac{\pi}{2}\)$
• D. $b=\(\pi\)$

Answer: (A)

Verified step by step guidance

1. The function given is y = sec(bx - π). The secant function, sec(x), has a period of 2π. Therefore, the period of sec(bx - π) is 2π/b.
2. From the graph, observe that the period of the function is π. This is the distance between two consecutive vertical asymptotes, for example, from x = π/2 to x = 3π/2.
3. Set the period of the function equal to the observed period from the graph: 2π/b = π.
4. Solve the equation 2π/b = π for b. This involves multiplying both sides by b and then dividing both sides by π.
5. After solving the equation, you will find that b = 2. This matches the observed period of the function on the graph.