When we talk about stretching and compressing functions, it might sound a little confusing at first. But don’t worry! Once you understand the basics, it’s actually pretty neat!

1. Stretching and Compressing:

   • Stretching a function means making it taller or longer. You usually do this by multiplying the function by a number larger than 1. For example, if you have a function called $f(x)$ and create a new one, $g(x) = 2f(x)$, you are stretching it to make it twice as tall. This means the high points (or peaks) of the graph will go up higher, and the low points (or valleys) will go lower.

   • Compressing a function is the opposite of stretching. Here, you multiply the function by a number between 0 and 1, like $g(x) = \frac{1}{2}f(x)$. This shortens the graph, so the high points drop closer to the x-axis.

2. Horizontal vs. Vertical:

   • When you multiply inside the function (like $f(kx)$ with $k > 1$), that’s called a horizontal compression. For example, $f(2x)$ makes the graph closer together horizontally.

   • On the other hand, if you are changing the function along the y-axis (like $kf(x)$), that’s a vertical stretch or compression. This depends on whether $k$ is bigger than or smaller than 1.

Overall, it’s important to know where to apply these stretches and compressions and how they change your graph!