1. Copyright © Cengage Learning. All rights reserved. Pre-Calculus Honors 3.1: Exponential Functions and Their Graphs

2. 2 Graphs of Exponential Functions y = 0 is a horizontal asymptote (a x  0 as x  ) Domain: (, ) (a –x  0 as x  )Range: (0, ) Continuous

3. 3 The Natural Base e For many applications, the convenient choice for a base is the irrational number e = 2.718281828.... This number is called the natural base. The function f (x) = e x is called the natural exponential function.

4. 4 Graph f(x) = 3 x. Label asymptote. Determine domain and range.

5. 5 Graph f(x) = 5 – e x. Label asymptote. Determine domain and range.

6. 6 Graph f(x) = 4 x – 2 – 3. Label asymptote. Determine domain and range.

7. 7 Graph f(x) =.5 -(x + 4). Label asymptote. Determine domain and range.

8. 8 Applications Exponential Growth/Decay:

9. 9 Example 8 – Finding the Balance for Compound Interest A total of $9000 is invested at an annual interest rate of 2.5%, compounded quarterly. Find the balance in the account after 5 years.