Learning Resources

Outcomes

In this lesson you will

• discover how changes in the equation of an exponential equation affect the shape and orientation of the curve
• discover a new transformation, the reflection in the y-axis, and how it affects the resulting graph

By the end of this section students will be able to:

• model real-world phenomena using exponential functions
• describe and interpret domains and ranges using set notation
• write exponential functions in transformational form and as mapping rules to visualize and sketch graphs
• analyze and describe the characteristics of exponential and logarithmic functions
• describe and translate between graphical, tabular, written, and symbolic representations of exponential and logarithmic relationships
• demonstrate an understanding of how parameter changes affect the graphs of exponential functions

Introduction

Mathematical Modeling, Book 3   p.143 - 155

You can now find an exponential function or equation from a table, graph or a specific description of a situation. In this section, transformations of the function, as learned in earlier courses, will be used to graph the more complex forms of the function. A new transformation, reflection in the y-axis, will be introduced and explored.

This section should take 4 hours to complete.

Prerequisites

To be successful in this lesson, it would be helpful to know the following:

• transformations and mapping rules
• asymptote
• reflection in y-axis