Exponential Function that passes through two given points

Visualize the exponential function that passes through two points, which may be dragged within the x-y plane.[br]Also see the resulting equation.
In the function f(x) = a b^x, what is the significance of the value of a in the graph?[br]When the function is increasing from left to right, what do you notice is always true about the equation? How about when the function is decreasing?[br]What needs to be true about the equation in order to make the graph pass through the third and fourth quadrants?

Information: Exponential Function that passes through two given points