Pre calc question

Question

Write an equation for a secant function with a period of 3𝜋 and a range of (−∞, −2] ∪ [2, ∞)

Answer 1

Model for secant is:

Asec(B(x+C)) + D , A= Amplitude, B= 2π/period, C = left phase shift and D = vertical shift

Normally the range for secant is y ≤ -1 or y ≥ 1, so A = 2 to match the criteria. D=0 and C=0.

B = 2π/3π = 2/3

y = 2sec(2x/3)