If the graph of f(x)=cotx is transformed by a horizontal shrink of 1/4 and a horizontal shift left pi, the result has what equation?
To find the equation of the transformed function, we need to apply the given transformations to the original function f(x) = cot(x).
1. Horizontal Shrink:
A horizontal shrink of 1/4 means compressing the graph horizontally by a factor of 1/4. This is done by multiplying the x-coordinate by 1/4.
2. Horizontal Shift:
A horizontal shift left by π units means shifting the graph π units to the left. This is done by subtracting π from the x-coordinate.
Let's apply these transformations step by step:
Horizontal Shrink:
The original function f(x) = cot(x) is compressed horizontally by a factor of 1/4. So the new function becomes f(4x) = cot(4x).
Horizontal Shift:
The horizontally shrunk function f(4x) = cot(4x) is now shifted π units to the left. So the new function becomes f(4x - π) = cot(4x - π).
Therefore, the equation of the transformed function is f(x) = cot(4x - π).