Exponential Functions Section 1. Exponential Function f(x) = a x, a > 0, a ≠ 1 The base is a constant and the exponent is a variable, unlike a power function.

Slides:

Advertisements

Similar presentations

State the domain and range of each function. 3.1 Graphs of Exponential Functions.

Advertisements

Exponential Functions Brought to you by Tutorial Services The Math Center.

6.3 Exponential Functions

Exponential Functions L. Waihman A function that can be expressed in the form A function that can be expressed in the form and is positive, is called.

Logarithmic Functions Section 3.2. Objectives Rewrite an exponential equation in logarithmic form. Rewrite a logarithmic equation in exponential form.

Basic Functions and Their Graphs

Logarithmic Functions. Definition of a Logarithmic Function For x > 0 and b > 0, b = 1, y = log b x is equivalent to b y = x. The function f (x) = log.

Logarithmic Functions Section 2. Objectives Change Exponential Expressions to Logarithmic Expressions and Logarithmic Expressions to Exponential Expressions.

1 6.3 Exponential Functions In this section, we will study the following topics: Evaluating exponential functions with base a Graphing exponential functions.

Exponential Functions Section 1. Exponential Function f(x) = a x, a > 0, a ≠ 1 The base is a constant and the exponent is a variable, unlike a power function.

How does one Graph an Exponential Equation?

Logarithmic Functions Section 3-2 Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 Definition: Logarithmic Function For x  0 and.

4.2 Logarithmic Functions

Definition of a Logarithmic Function For x > 0 and b > 0, b≠ 1, y = log b x is equivalent to b y = x The function f (x) = log b x is the logarithmic function.

Sullivan PreCalculus Section 4.4 Logarithmic Functions Objectives of this Section Change Exponential Expressions to Logarithmic Expressions and Visa Versa.

Exponential and Logarithmic Functions and Equations

Section 6.3. This value is so important in mathematics that it has been given its own symbol, e, sometimes called Euler’s number. The number e has many.

Aim: What is an exponential function?

Objectives: Evaluate Exponential Functions Graph Exponential Functions Define the Number e.

Exponential Functions. Exponential Functions and Their Graphs.

Exponential Functions L. Waihman A function that can be expressed in the form A function that can be expressed in the form and is positive, is called.

Exponential and Logarithmic Functions Exponents and Exponential Functions Exponential and Logarithmic Functions Objectives Review the laws of exponents.

Section 6.3 – Exponential Functions Laws of Exponents If s, t, a, and b are real numbers where a > 0 and b > 0, then: Definition: “a” is a positive real.

Sullivan Algebra and Trigonometry: Section 5.3 Exponential Functions Objectives of this Section Evaluate Exponential Functions Graph Exponential Functions.

Asymptote. A line that the graph of a curve approaches but never intersects. Add these lines to your graphs!

Exponential Functions MM3A2e Investigate characteristics: domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, rate of.

6.3 Logarithmic Functions. Change exponential expression into an equivalent logarithmic expression. Change logarithmic expression into an equivalent.

6.2 Exponential Functions. An exponential function is a function of the form where a is a positive real number (a > 0) and. The domain of f is the set.

State the domain and range of each function Exponential Growth and Decay.

Exponential Functions What You Will Learn How to graph exponential functions And how to solve exponential equations and inequalities.

One-to-One Property Section 3.1 Exponential Functions.

Exponential Functions Evaluate Exponential Functions Graph Exponential Functions Define the number e Solve Exponential Equations.

Exponential Functions Algebra III, Sec. 3.1 Objective Recognize, evaluate, and graph exponential functions.

9.1 Exponential Functions

Logarithms 2.5 Chapter 2 Exponents and Logarithms 2.5.1

Logarithmic Functions Just another way to write exponents.

5.2 Logarithmic Functions & Their Graphs Goals— Recognize and evaluate logarithmic functions with base a Graph Logarithmic functions Recognize, evaluate,

Section 5.4 Logarithmic Functions. LOGARITHIMS Since exponential functions are one-to-one, each has an inverse. These exponential functions are called.

SECTION 4.3 EXPONENTIAL FUNCTIONS EXPONENTIAL FUNCTIONS.

Slide Copyright © 2012 Pearson Education, Inc.

4.3 – Logarithmic functions

Exponential Functions

 A function that can be expressed in the form and is positive, is called an Exponential Function.  Exponential Functions with positive values of x are.

Exponential Growth Exponential Decay Example 1 Graph the exponential function given by Solution xy or f(x) 0 1 –1 2 – /3 9 1/9 27.

Exponential Functions Chapter 10, Sections 1 and 6.

Math – Exponential Functions

Section Vocabulary: Exponential function- In general, an equation of the form, where, b>0, and, is known as an exponential function. Exponential.

LEQ: How do you evaluate logarithms with a base b? Logarithms to Bases Other Than 10 Sec. 9-7.

Graphs of Exponential Functions. Exponential Function Where base (b), b > 0, b  1, and x is any real number.

Objectives: The student will be able to… 1)Graph exponential functions. 2)Solve exponential equations and inequalities.

Graphing Exponential and Logarithmic Functions. Objective I can graph exponential functions using a graphing utility and identify asymptotes, intercepts,

Copyright © 2011 Pearson Education, Inc. Logarithmic Functions and Their Applications Section 4.2 Exponential and Logarithmic Functions.

Logarithmic Functions & Their Graphs Goals— Recognize and evaluate logarithmic functions with base a Graph Logarithmic functions Recognize, evaluate, and.

Sullivan Algebra and Trigonometry: Section 6.4 Logarithmic Functions

Exponential Functions

Sullivan Algebra and Trigonometry: Section 6.3 Exponential Functions

Sullivan Algebra and Trigonometry: Section 6.3

How does one Graph an Exponential Equation?

Logarithmic Functions and Their Graphs

6.3 Logarithmic Functions

4.2 Exponential Functions

6.2 Exponential Functions

Exponential Functions

4.2 Exponential Functions

6.9 Graphing Exponential Equations

4.3 Logarithmic Functions

Sullivan Algebra and Trigonometry: Section 6.2

4.3 Logarithmic Functions

7.4 Graphing Exponential Equations

Presentation transcript:

Exponential Functions Section 1

Exponential Function f(x) = a x, a > 0, a ≠ 1 The base is a constant and the exponent is a variable, unlike a power function.

For an exponential function f(x) = a x, a > 0, a ≠ 1, if x is any real number, then

Page

Properties of the Exponential Function when a > 1 Domain: All reals Range: Positive reals No x-intercepts y-intercept: 1 x-axis is a horizontal asymptote as x  -∞ Increasing function One-to-one Graph contains the points (0, 1), (1, a), and (-1, 1/a) Graph is smooth and continuous, with no corners or gaps

Example: Graph the following equations on your calculator: y 1 = 2 x y 2 = 3 x y 3 = 5 x For what values of x is 2 x < 3 x < 5 x ? For what values of x is 2 x > 3 x > 5 x ? For what values of x is 2 x = 3 x = 5 x ?

Properties of the Exponential Function when 0 < a < 1 Domain: All reals Range: Positive reals No x-intercepts y-intercept: 1 x-axis is a horizontal asymptote as x  ∞ Decreasing function One-to-one Graph contains the points (0, 1), (1, a), and (- 1, 1/a) Graph is smooth and continuous, with no corners or gaps

Example: Graph the following equations on your calculator: y 1 = (1/2) x y 2 = (1/3) x y 3 = (1/5) x For what values of x is (1/2) x < (1/3) x < (1/5) x ? For what values of x is (1/2) x > (1/3) x > (1/5) x ? For what values of x is (1/2) x = (1/3) x = (1/5) x ?

Graphing Using Transformations Page

Pages (22-44 even, 75, 77, 79, 85)

The number e is defined as the number that the expression approaches as n  ∞

Page 503 #45

Solving Exponential Equations If a u = a v, then u = v

Page

Page

Page

Pages (46-70 even)