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.

Slides:

Advertisements

Similar presentations

Graph of Exponential Functions

Advertisements

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

Finding the Intercepts of a Line

Graphs of Equations Finding intercepts of a graph Graphically and Algebraically.

Graphs of Exponential and Logarithmic Functions

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

Create a table and Graph:. Reflect: Continued x-intercept: y-intercept: Asymptotes: xy -31/3 -21/2 1 -1/22 xy 1/ /2 3-1/3.

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

Intercepts, Exponentials, and Asymptotes Section 3.4 Standard: MCC9-12.F.IF.7a&e Essential Question: How do you graph and analyze 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.

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.

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

Lesson 5-6: Logarithms and Logarithmic Functions

How do I graph and use exponential growth and decay 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.

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.

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.

Mrs. McConaughyHonors Algebra 21 Graphing Logarithmic Functions During this lesson, you will:  Write an equation for the inverse of an exponential or.

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.

Logarithmic Functions. Objective To graph logarithmic functions To graph logarithmic functions To evaluate logatrithms To evaluate logatrithms.

For the function determine the following, if it exists. 1.Vertical asymptotes 2.Horizontal asymptotes 3.Oblique asymptotes 4.x-intercepts 5.y-intercept.

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

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.

Real Exponents Chapter 11 Section 1. 2 of 19 Pre-Calculus Chapter 11 Sections 1 & 2 Scientific Notation A number is in scientific notation when it is.

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

Exponential GrowthExponential Decay (0,a) Exponential Parent Fcn: Growth: b > 1 Decay: 0 < b < 1 H.Asymptote: y = 0 y-int is a_(1 on parent fcn) Shifts:

Equations of Lines Standard Form: Slope Intercept Form: where m is the slope and b is the y-intercept.

9.1 Exponential Functions

Logarithms 2.5 Chapter 2 Exponents and Logarithms 2.5.1

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.

4.3 – Logarithmic functions

Exponential Functions

Exponential Functions Exponential Growth Exponential Decay y x.

Warm-Up 1. Write the following in Slope-Intercept From: 2. Given the following table, write the exponential model: X01234 Y

 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.

Math 71B 9.3 – Logarithmic Functions 1. One-to-one functions have inverses. Let’s define the inverse of the exponential function. 2.

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.

Unit 3. Day 10 Practice Graph Using Intercepts.  Find the x-intercept and the y-intercept of the graph of the equation. x + 3y = 15 Question 1:

Graph Y-Intercept =(0,2) Horizontal Asymptote X-Axis (y = 0) Domain: All Real Numbers Range: y > 0.

Exponential Function. 1. Investigate the effect of a =+/-1 on the graph : 2. Investigate the effect of a on the graph: 3. Investigate the effect of q.

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.

Twenty Questions Rational Functions Twenty Questions

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.

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.

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

Exponential Equations

6.3 Logarithmic Functions

4.2 Exponential Functions

6.2 Exponential Functions

Logarithmic Functions

4.2 Exponential Functions

4.3 Logarithmic Functions

Sullivan Algebra and Trigonometry: Section 6.2

4.3 Logarithmic Functions

Warm-up: Solve each equation for a. 1. 2a–b = 3c

Presentation transcript:

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 of all real numbers.

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

Summary of the characteristics of the graph of a >1 The domain is all real numbers. Range is set of positive numbers. No x-intercepts; y-intercept is 1. The x-axis (y=0) is a horizontal asymptote as a>1, is an increasing function and is one-to-one. The graph contains the points (0,1); (1,a), and (-1, 1/a). The graph is smooth continuous with no corners or gaps.

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

Summary of the characteristics of the graph of 0 <a <1 The domain is all real numbers. Range is set of positive numbers. No x-intercepts; y-intercept is 1. The x-axis (y=0) is a horizontal asymptote as 0<a<1, is a decreasing function and is one-to-one. The graph contains the points (0,1); (1,a), and (-1, 1/a). The graph is smooth continuous with no corners or gaps.

(0, 1) (1, 3)

(0, 1) (-1, 3)

(0, 3) (-1, 5) y = 2

Horizontal Asymptote: y = 2 Range: { y | y >2 } or Domain: All real numbers

The number e is defined as the number that the expression In calculus this expression is expressed using limit notation as

Exponential Equations

Solve: