The original function in this problem is f(x) = 2^x. We need to apply two transformations to this function, a vertical stretch by a factor of six, and then a reflection across the x-axis.
First, let's apply the vertical stretch. In the context of functions, a "vertical stretch" means that we multiply the original function by some factor. In this case, the stretch factor is six. So, to perform this transformation, take the original function 2^x and multiply it by 6. Our function becomes:
f(x) = 6*(2^x)
Now we have stretched our function vertically by a factor of six.
The second transformation we need to apply is a reflection across the x-axis. To accomplish this, we multiply the entire function by -1. This is because changing the sign of a function reflects it across the x-axis. Therefore, multiply the function f(x) = 6*(2^x) by -1.
f(x) = -1 * [6*(2^x)] = -6*2^x
So, the original function 2^x, after a vertical stretch by a factor of 6 and a reflection across the x-axis, transforms and becomes -6*2^x.