Unit 7: Exponential and Logarithmic Functions
Welcome to the final unit on functions. In this unit, you will learn about exponential and logarithmic functions. Exponential functions are often used to model the behavior of populations and the growth of an investment or debt. You will learn the characteristics of an exponential function and become proficient at graphing them given key components. In addition to exponential functions, you will learn about the logarithmic function. The logarithmic function is the inverse of the exponential, and we will explore the relationship between the two.
Completing this unit should take you approximately 3 hours.
Upon successful completion of this unit, you will be able to:
- evaluate exponential and logarithmic functions;
- define the equation for exponential and logarithmic functions given a graph or data points;
- identify properties of exponential and logarithmic equations, including asymptotes, long run, and local behavior;
- graph exponential and logarithmic equations using transformations;
- identify the domain and range of exponential and logarithmic functions; and
- summarize the inverse relationship between exponential and logarithmic functions.
7.1: Intorduction to Exponential Functions
- First, we will see how to identify an exponential function given an equation, a graph, and a table of values. You will be able to determine whether an exponential function is growing or decaying over time and how to define its domain and range.
- In this section on exponential functions, you will determine the equation of an exponential function given two points or a graph.
In the last section on exponential functions, you will learn how to apply the compound interest formula and explore continuous growth.
7.2: Graphs of Exponential Functions
This section will define the key characteristics of the graph of an exponential function, including horizontal asymptotes, long-run behavior, and intercepts.
In this section, you will apply what you know about transformations of functions to graphs of exponential functions. You will perform vertical and horizontal shifts, reflections, stretches, and compressions. You will also investigate how these transformations affect the equation, its domain and range, and the end behavior of the function.
7.3: Introduction to Logarithmic Functions
Logarithms are the inverses of exponential functions. You will explore the relationship between an exponential and a logarithmic function. You will also explore the basic characteristics of a logarithmic function, including domain, range, and long-run behavior.
In this section on logarithmic functions, you will explore logarithms with base ten and base e and how they are related to their inverse exponential functions.
7.4: Graphs of Logarithmic Functions
Now, we will define the domain and range of a logarithmic function given an equation or a graph. We will also construct graphs of logarithmic functions given tables and equations.
Finally, we will transform the graph of logarithmic functions using vertical and horizontal shifts, reflections, and compressions and stretches. Given the graph of a logarithmic function, we will practice defining the equation.
7.5: Properties of Logarithmic Functions
Before diving into solving logarithmic and exponential equations, it is helpful to know the properties of logarithms because they can help you out of tricky situations. In this section, you will learn the algebraic properties of logarithms, including the power, product, and quotient rules.
Finally, we will wrap up the properties of logarithms by learning how to expand and condense logarithms and use the change of base formula.