Graph of Exponential Functions Chapter 3 Lesson G

Exponential Functions The general exponential function has form f(x) = a^x where a>0, a≠1 y=0 is a horizontal asymptote

Example Graph y= 2^x

General Exponential Function y= a x b ^(x-c) +d b controls how steeply the graph increases or decreases c controls horizontal translation D controls vertical translation and y=d is the equation of the horizontal asymptote

General Exponential Function If a>0, b>1 If a>0, 0<b<1 If a<0, b>1 If a<0, 0<b<1

Horizontal Asymptotes y= a x b ^(x-c) +d In this function y=d is the horizontal asymptote Using these you can obtain a reasonably accurate sketch of the graph Horizontal asymptote Y-intercept Two other points, say when x=2, x=-2

Example

Homework Page 77-78 #1-5