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

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)