Compressions can really change how we see graphs of functions! When we talk about compressions, we mean how the graph gets squished either from side to side or up and down. This can really change how the graph looks.

Horizontal Compression

• How it works: When we have a function, let's say ( f(x) ), and we want to compress it from the sides, we can use a factor called ( k ) (where ( k > 1 )). We write it as ( f(kx) ).
• What happens: The graph becomes narrower. For example, if we start with ( f(x) = x^2 ) and change it to ( f(2x) ), the graph will look steeper and closer to the y-axis.

Vertical Compression

• How it works: For compressing the graph up and down, we change the function to ( c f(x) ), where ( 0 < c < 1 ).
• What happens: The graph looks flatter. So if we take ( f(x) = x^2 ) and change it to ( f(0.5x) ), the graph will stretch upwards but also get wider, making it look more spread out.

See the Changes

It’s really helpful to draw these changes next to each other. You can see how horizontal compressions pull the graph in and vertical compressions change how high it goes.

In the end, trying out these different transformations helps you understand functions better! You’ll learn what makes each graph special!