Sullivan Algebra and Trigonometry: Section 5.3 Exponential Functions 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 On a scientific calculator: 2 yxyx 1.41 On a graphing calculator: 2 ^ =

The graph of a basic exponential function can be readily obtain using point plotting. (0, 1) (1, 3) (1, 6) (-1, 1/3) (-1, 1/6) 3x3x 6x6x

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, 3) (-1, 6) (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)

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

Solve the following equations for x.