Absolutely! Let’s jump into the fun world of function transformations and learn about the differences between compression and stretch!

What is Compression?

• Definition: Compression happens when a function is "squished" or squeezed toward the y-axis.
• Effect: This makes the graph look narrower!
• Example: For the function ( f(x) = x^2 ), if we compress it vertically by a factor of (\frac{1}{2}), it changes to ( g(x) = \frac{1}{2}x^2 ).

What is Stretch?

• Definition: Stretch is when a function is "pulled" away from the y-axis.
• Effect: The graph looks wider!
• Example: Using the same function, if we stretch it vertically by a factor of 2, it changes to ( g(x) = 2x^2 ).

Summary

• Compression: The graph becomes narrower when (0 < k < 1).
• Stretch: The graph becomes wider when (k > 1).

Isn’t it cool how these transformations change the shape of the graph? Keep exploring and have fun learning about functions! 🎉