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.
Accepted Solution
A:
First lets look at our graph of y = cos x ***First picture***
Next lets look at a vertical stretch. ***Second picture***
To vertically stretch y = cos x, we need to multiply cos by a number greater than 1. I am going to use 2.
Standard Form: y = cos x (Red Line) Vertical Stretch: y = 2 cos x (Blue Line)
Lets look at a vertical shrink ***Third picture***
To create a vertical shrink, you multiply the cos by a number less than 1. I am going to use .5
Standard Form: y = cos x (Red Line) Vertical Shrink: y = .5 cos x (Green Line)
Now lets look at horizontal stretch. ***Forth picture.***
To create a horizontal stretch, you multiply the x by a value less than 1. I am going to use .5
Standard Form: y = cos x (Red Line) Vertical Stretch: y = .5 cos x (Orange Line)
Finally, to create a horizontal shrink, you multiply the x by a value greater than 1. I am going to use 2. ***Fifth picture.***
Standard Form: y = cos x (Red Line) Vertical Shrink: y = 2 cos x (Purple Line)