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 - Graphsand
Logarithmic Functions - Graphs.
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)Print this page