When you think about vertical stretches on function graphs, it’s all about how the graph gets “pulled” up or down.

If you take a function, like $f(x)$, and multiply it by a number bigger than 1, you create a vertical stretch.

For example, if you have $2f(x)$, every point on the graph of $f(x)$ is stretched away from the x-axis by a factor of 2.

Here’s What Happens with Vertical Stretches:

1. Graph Gets Taller: The entire graph becomes taller. Points that were at a certain height on the graph now move up higher. For example, if the original point is $(1, 3)$, after stretching, it turns into $(1, 6)$.

2. X-Values Stay the Same: The x-coordinates don’t change at all. The stretching only makes the points go higher or lower.

3. Only Positive Numbers: We only multiply by positive numbers, so the graph keeps going in the same direction (up or down) as the original function.

4. Shape Remains the Same: Even though the graph stretches, it doesn't change its shape. It just looks taller! This means important parts of the graph, like where it touches the axes, also change in a similar way.

In short, vertical stretches can transform your graph while keeping its basic shape intact. It’s a fun change to explore!