Algebra II: Logarithmic Transformations

Objectives

Change the parameters of the logarithmic function y=a*log(b(x - h))+ k to discover that changes in:

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

Vocabulary

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

About the Lesson

This lesson involves graphing logarithmic functions of the form y = a* log(b(x - h)) + k. As a result, students will:

• Manipulate given parameters and make conjectures about the relationships between the parameters’ values and the effects on the graph of the resulting logarithmic function.
• Test knowledge and determine the logarithmic function for a given graph.