Graph exponential functions and explore by making changes in the parameters.

Change the parameters of the exponential function to discover that changes in:

• k result in vertical translations
• h result in horizontal translations
• a result in vertical stretches and compressions (dilations), and reflections across the x-axis
• b result in horizontal stretches and compressions (dilations), and reflections across the y-axis

• Translation
• Dilation
• Compression
• Stretch
• Reflection
• Transformation

This lesson involves graphing exponential functions of the form y = a*base^{b*(x - h )} - k. As a result, students will:

• Manipulate given parameters and make conjectures about the relationships between the parameters’ values and their effects on the resulting exponential function’s graph.
• Test their newly-learned knowledge and determine the exponential function for a given graph.