This interactive allows you to change the base and shift the function.
h represents the horizontal shift of the exponential function.
k represents the vertical shift of the exponential function.
You may use the sliders to change the base, h, and k, or simply put in specific values into the boxes.
In the third quadrant you have boxes that you can check or uncheck depending on what you want to see or hide.
The following questions are asked:
By definition of exponential functions, the base cannot be 1. What happens to the graph of the exponential function when base = 1?
By definition of logarithmic functions, the base cannot be 1. What happens to the graph of the logarithmic function when base = 1?
Changing h changes the horizontal position of the exponential function. What does it do to the logarithmic function and why?
Changing k changes the vertical position of the exponential function. What does it do to the logarithmic function and why?
For what bases is the exponential function increasing?
For what bases is the exponential function decreasing?
For what bases is the logarithmic function increasing?
For what bases is the logarithmic function decreasing?
What generalization can be made about the inverse of an increasing one-to-one function?
What generalization can be made about the inverse of a decreasing one-to-one function?
