Which function is represented in this graph?

y = tan (1/2 x - π/2) ⇒ the answer is (b)

Step-by-step explanation:

* Lets talk about the tangent function

- The tangent has a period of π, with each period separated by

 a vertical asymptote. The concept of "amplitude" doesn't

  really exist because -∞ < y < ∞

- You can transform the graph for tangent

∵ y = A tan B(x + C) + D

* Where:

# A, changes amplitude. (A always = 1)

# B determines the period.

# C determines how the graph is shifted from left to right.

  (horizontally)

# D determines how the graph is shifted up or down.(vertically)

∵ The basic function is y = tanФ has an amplitude of 1.

   It has a period of π. It has no phase or vertical shifts,

   because it is centered on the origin.

* Look to the problem

- From the graph:

- The period is 2π

∵ Period = π/B

∴ 2π = π/B ⇒ ÷ π

∴ 2 = 1/B

∴ B = 1/2

- the starting point of the function is at π instead of zero

∴ It moves π units to the right

∴ C = -π

∴ y = tan 1/2(x - π)

∴ y = tan (1/2 x - π/2)

* The function is ⇒ y = tan (1/2 x - π/2)

* The blue represents y = tanx

  The red represents y = tan (1/2 x - π/2)

answer: r there any options?

step-by-step explanation: