Tangent has no maximum or minimum (its range is (-∞,∞)). There is no amplitude.
x is an integer applied to the angle 3π/2. The tangent of any odd multiple of 3π/2 is indeterminate (plus or minus infinity). Even multiples have a tangent of zero.
y=tan(x) is the "parent" function. tan(πx)=0, for integer x, so it repeats itself at integer steps. Therefore tan(3πx) repeats itself 3 times more frequently, making its period=⅓.
Answer b.