Prompt Title: I'm just trying to study

Sure! Let's consider the function f(x) = x^2. Suppose we want to scale this function vertically by a factor of 2. To do this, we would multiply each y-value by 2.

To see how this transformation affects the graph of the function, let's make a table of values and graph the original function and the transformed function side by side:

The original function is shown in the first column of the table, and the transformed function is shown in the second column. Notice that for each value of x, the y-value of the transformed function is twice the y-value of the original function.

Now let's graph the two functions on the same coordinate plane:

Original function (in blue):

Transformed function (in red):

As you can see, the transformation vertically stretched the function by a factor of 2. Each point on the original function was mapped to a point on the transformed function with twice the y-coordinate.

In general, scaling a function vertically by a factor of a simply multiplies each y-value by a. So, if we have a function f(x), and we want to scale it vertically by a factor of a, the transformed function g(x) would be:

g(x) = a * f(x)

I hope this helps! Let me know if you have any more questions or if you'd like me to explain anything in more detail.