Chapter 12 Logarithmic Exponential Functions Section 1 Exponential

Chapter 12 Logarithmic & Exponential Functions Section 1 Exponential Functions Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 1

Study Strategy Study Groups üAssess Your Knowledge Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 2

Concept Exponential Function A function of the form and is called an exponential function. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 3

Example 1 Exponential Function For find Copyright © 2016, 2012, and 2009 Pearson Education, Inc. and 4

Concept The Natural Exponential Function The function is the natural exponential function, where Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 5

Example 2 The Natural Exponential Function For find Round to the nearest thousandth. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 6

Concept Graphing Exponential Functions For an exponential function · Graph the horizontal asymptote using a dashed line. · Create a table of values centered around · Draw the graph passing through the points. The domain of the function is the set of all real numbers, but the range is restricted. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 7

Example 3 Graphing Exponential Functions (page 1) Graph: Horizontal Asymptote: x 0 f(x) 1 2 3 4 Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 8

Example 3 Graphing Exponential Functions (page 2) Domain: Range: Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 9

Concept One-to-One Property of Exponential Functions For any positive real number b and any real numbers x and y, if then Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 10

Example 4 One-to-One Property of Exponential Functions Solve: Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 11