Answer:
y = -3cos(2(x -1)) -1
Explanation:
You want a cosine function with an amplitude of 3, a period of π, and a minimum at (1, -4).
Scaling
The amplitude factor multiplies the cosine function, so it will be 3cos( ). The parent cosine function has a maximum at x=0. In order to have the minimum at x=0, we need the scale factor to be -3: -3cos( ).
The argument of the cosine function is 2πx/period. Since we want the period to be π, the argument will be (2πx/π) = 2x.
Then our scaled cosine function is ...
-3cos(2x)
Translation
This function will have a minimum at (0, -3). We want to move the minimum to (1, -4), which is 1 unit right and 1 unit down.
Translation of a function f(x) by (h, k) units (right, up) makes it become ...
f(x -h) +k
For (h, k) = (1, -1), the above cosine function becomes ...
y = -3cos(2(x -1)) -1
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