Hi everyone! Read through the material below, watch the videos, and send me your questions.

Lesson 13: Exponential and Logarithmic Functions

Topic: This lesson covers Chapter 13 in the book, Exponential and Logarithmic Functions.

WeBWorK: There are two WeBWorK assignments on today’s material: Exponential Functions - Graphs and Logarithmic Functions - Graphs .

#### Lesson Notes (Notability – pdf):

This .pdf file contains most of the work from the videos in this lesson. It is provided for your reference.

## Exponential Functions and their Graphs

We’ve been living in the world of Polynomials and Rational Functions. We now turn to exponential functions. These functions are “very natural” – that is, they show up in the real world – but they are also more complicated than Polynomial and Rational functions (for example, an exponential function grows more quickly than any Polynomial)

Definition. An exponential function is a function of the form , where and are real numbers and is positive ( is called the base, is the exponent).

Example 1 (Textbook 13.2): Graph the exponential functions .

Now let’s see what happens when we change the number in .

Example 2 (Textbook 13.6): Graph the exponential functions
a) b) c) d) e) Example 3: The graph below shows an exponential function . Find a formula for .

## Logarithmic Functions and their Graphs

Definition. If is a positive real number and , then the logarithm with base is defined: What does the definition of logarithm mean? The idea is that the logarithm is the inverse function of the exponential function. Let’s look at an example.

Question: Is an exponential function one-to-one? (What does one-to-one means).

Example 4. The graph below shows the function but shifted to the right 3 units. Find a formula for the function in the graph.

That’s it for now! Take a look at the WeBWorK assignment, leave your questions below (or use the Ask for Help button in WeBWorK, or send me an email)