Sullivan Algebra and Trigonometry: Section 6.2 Objectives of this Section Evaluate Exponential Functions Graph Exponential Functions Define the Number e Solve Exponential Equations

An exponential function is a function of the form where a is a positive real number (a > 0) and a 1. The domain of f is the set of all real numbers.

Using a calculator to evaluate an exponential function Example: Find 2 1.41 On a scientific calculator: 2 yx 1.41 On a graphing calculator: 2 ^ 1.41 2 1.41 = 2.657371628...

The graph of a basic exponential function can be readily obtain using point plotting. (1, 6) 6x 3x (1, 3) (-1, 1/3) (-1, 1/6) (0, 1)

Summary of the Characteristics of the graph of Domain: All real numbers Range: (0, ) No x-intercepts y-intercept: (0,1) Horizontal asymptote: y = 0 as x Increasing function One-to-one

Summary of the Characteristics of the graph of Domain: All real numbers Range: (0, ) No x-intercepts y-intercept: (0,1) Horizontal asymptote: y = 0 as x Decreasing function One-to-one

(-1, 6) (-1, 3) (0, 1) (1, 1/3) (1, 1/6)

Graph and determine the domain, range, and horizontal asymptote of f. (0, 1) (1, 3) (0, 1) (-1, 3)

Domain: All real numbers (-1, 5) (0, 3) y = 2 Domain: All real numbers Range: { y | y >2 } or (2, ) Horizontal Asymptote: y = 2

Solve the following equations for x.