Answer:
Period = 4 units
Step-by-step explanation:
Standard form of a tangent function:
[tex]f(x)=\sf A \tan(B(x+C))+D[/tex]
- 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:
[tex]y=\tan \left(\dfrac{\pi}{4}\left(x-\dfrac{\pi}{3}\right)\right)[/tex]
Therefore:
- Vertical stretch (A) = none
- [tex]\textsf{Period}=\dfrac{\pi}{\left|\dfrac{\pi}{4}\right|}=4[/tex]
- Phase shift (C) = π/3 to the right
- Vertical shift = none
