Question

Which transformation causes the described change in the graph of the function y = cos x?
The transformation______results in a horizontal shrink.

The transformation_____results in a vertical stretch.

The transformation ____ results in a horizontal stretch.

The transformation_____results in a vertical shrink.

Answer 1

Horizontal Shrink: y = cos 2x or if the coefficient of x is greater than 1
Vertical Stretch: y = 2 cos x or if the coefficient if cos x is greater than 1
Horizontal Stretch: y = cos (1/2) x or if the coefficient of x is less than 1
Vertical Shrink: y = (1/2) cos x or the coefficient of cos x is less than 1

The base value is 1 since it is the original coefficient of x and cos x. The values would adjust depending on the original coefficients.