Exploring Exponential Growth and Decay

Below is the graph of the function f(x) = a b^x. Adjust the sliders to change the values of a and b. What happens as a gets larger? As a gets smaller? As a is less than 0?

What happens when b>1? What can you say about the behavior of the graph of exponential growth functions as x tends towards ∞? -∞?

What happens when 0 < b < 1? What can you say about the behavior of the graph of exponential growth functions as x tends towards ∞? -∞?

Match each function with the given graph.