Question

What is the period of the function y=tan (4/pi (x-pi/3))

O 3 units
O4 units
O 6 units
O 8 units

Answer 1

Answer: 4 units

Explanation:

Answer 2

Period = 4 units

Explanation:

Standard form of a tangent function:

`f(x)=\sf A \tan(B(x+C))+D`

• A = vertical stretch
• π / |B| = period (distance between any two consecutive vertical asymptotes)
• C = phase shift (horizontal shift - positive is to the left)
• D = vertical shift

The tangent function has a vertical asymptote whenever cos(x) = 0

The tangent function does not have an amplitude because it has no maximum or minimum value.

Given function:

`y=\tan \left((\pi)/(4)\left(x-(\pi)/(3)\right)\right)`

Therefore:

• Vertical stretch (A) = none
• 
  `\textsf{Period}=(\pi)/(\left|(\pi)/(4)\right|)=4`
• Phase shift (C) = π/3 to the right
• Vertical shift = none