Introduction to exponential functions

INTRODUCTION TO EXPONENTIAL FUNCTIONS Instructor: Mohammad Mashayekhi

Outline: ■ Introduction to exponential functions ■ Properties of exponential functions ■ Behavior of exponential functions for large x values

Introduction to exponential functions: Exponential functions are defined as:

𝑓 𝑥 = 𝑎 % 𝑓𝑜𝑟 𝑎 > 0

§ 𝑓 𝑥 = 𝑒 % is probably the most popular exponential function in calculus! In this function, 𝑎 = 𝑒 ≃ 2.71 which is known as Euler’s constant or Napier’s constant. § Note that the domain for exponential function is ℝ and the range is only positive numbers!

Exponential functions are defined as:

Properties: ■ 𝑎2 = 1 ■ 𝑎 % 𝑎 3 = 𝑎 %43 ■ (𝑎𝑏)% = 𝑎 % 𝑏 % ■ 𝑎8% =

9 :;

■ (𝑎 % )3 = 𝑎 %.3
0

𝑓 𝑥 = 2% g 𝑥 = 𝑒% h 𝑥 = 3%

Behavior of exponential functions for large x values: 𝑓 𝑥 = 𝑎 % ,

𝑓 𝑥 = 𝑎 % ,

𝑎>1

1 2

%

2%

𝑎