identify the amplitude and period of this function: y=1/4tan(3pi)x

Question

Identify the amplitude and period of this function: 1/4tan(3pi)x.

a. 1/4, 3^pi

b. none because no maximum or minimum value exist; 1/3

c. n is an integer, 1/4

d. none because no maximum or minimum value exist; 1/3 pi

Answer 1

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.