Question

Please help.. I don't understand this question and the assignment is due tomorrow.

Answer 1

Answer:

y = 7 csc(½ x) − 2

Step-by-step explanation:

General form of a cosecant function is:

y = A csc(2π/T x + B) + C

where A is the amplitude, T is the period, B is the horizontal offset ("phase shift"), and C is the vertical offset ("midline").

The range is (-∞, -9] [5, ∞), so the midline is halfway between -9 and 5.

C = (-9 + 5) / 2

C = -2

The amplitude is half the difference between -9 and 5.

A = |-9 − 5| / 2

A = 7

The period is twice the distance between consecutive asymptotes.

T = 2 (2π − 0)

T = 4π

So far, we have:

y = 7 csc(½ x + B) − 2

We know there is an asymptote at x = 0.  Cosecant is undefined at multiples of π, so:

½ (0) + B = kπ

B = kπ

B is any multiple of π.  The simplest choice is B = 0.

y = 7 csc(½ x) − 2