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