Final answers
A) Graph the function: y = 3 cot(4x + π) - 1
B) Movable black point
C) Red point
D) Blue point
E) Verify coordinates
Step-by-step explanation
The given function is y = 3 cot(4x + π) - 1. To graph it, follow these steps:
Firstly, plot the primary points by observing the key characteristics of the function. For the cotangent function, identify vertical asymptotes at odd multiples of π in the form of x = (n * π) / 4, where n is an integer. Also, note the period of the function, which is π / 4. Plot these critical points and asymptotes accordingly.
Secondly, consider the amplitude and vertical shift. The amplitude for cotangent is 3, and there's a vertical shift of -1. This affects the range and the position of the curve vertically.
Lastly, connect the plotted points smoothly, keeping in mind the periodicity and behavior of the cotangent function between asymptotes. The resulting graph represents y = 3 cot(4x + π) - 1.