Question

1)if the graph of f(x)=cotx is transformed by a horizontal shrink of 1/4 and a horizontal shift left pi, the result is the graph of:
a) g(x)= cot[1/4(x-pi)] b) g(x)=cot[1/4(x+pi)]
c) g(x)=cot[4(x-pi)] d) g(x)=cot[4(x+pi)]
e) g(x)=cot[4x+pi]

please include how you got the answer

Answer 1

The standard cotangent function y = cot x
has a period of π radians , or form 0 to π there will be one complete cotangent curve.
So a "horizontal shrink of 1/4" I read that as having a period of π/4, or there will be 4 complete cotangent curves from 0 to π
this would give us a new function of
y = cot (4x)

now we shift this to the left π units, for a final equation of
y = cot 4(x+π) , which looks like d)

Answer 2

Thanks