One focus of the AP Pre-Calculus core is the relationship between exponential and logarithmic functions. During this session, we will explore, using tasks and technology, how this inverse relationship can be extended to transformations (vertical and horizontal shifts as well as dilations) of these functions. We will discover why any exponential function is a dilation of any other exponential function and why any logarithmic function is a dilation of any other logarithmic function. Finally, we will unwrap the rates of change of exponential and logarithmic functions to discover why the rate of change for any exponential function is also an exponential function and why the rate of change for any logarithmic function is a dilated rational function. This work serves as a precursor to derivatives of exponential and logarithmic functions in AP Calculus AB and BC.
