Sec. 4.1-4.3. Write the expression using logs: 2 x =7.2.

Slides:



Advertisements
Similar presentations
3.4 Inverse Functions & Relations
Advertisements

Logarithmic Functions
Exponential and Logarithmic Functions
Graph of Exponential Functions
3.2 Inverse Functions and Logarithms 3.3 Derivatives of Logarithmic and Exponential functions.
Rational Expressions, Vertical Asymptotes, and Holes.
Graphs of Exponential and Logarithmic Functions
1.6 – Inverse Functions and Logarithms. One-To-One Functions A function is one-to-one if no two domain values correspond to the same range value. Algebraically,
5.2 Logarithmic Functions & Their Graphs
Logarithmic Functions Section 2. Objectives Change Exponential Expressions to Logarithmic Expressions and Logarithmic Expressions to Exponential Expressions.
Section4.2 Rational Functions and Their Graphs. Rational Functions.
Functions and Graphs.
7.4 Logarithms p. 499 Evaluate logarithms Graph logarithmic functions
Sullivan PreCalculus Section 4.4 Logarithmic Functions Objectives of this Section Change Exponential Expressions to Logarithmic Expressions and Visa Versa.
SFM Productions Presents: Another saga in your continuing Pre-Calculus experience! 3.2Logarithmic Functions and their Graphs.
MAC 1105 Section 4.3 Logarithmic Functions. The Inverse of a Exponential Function 
Logarithms.
Logarithmic Functions Section 8.4. WHAT YOU WILL LEARN: 1.How to evaluate logarithmic 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.
Sullivan Algebra and Trigonometry: Section 5.3 Exponential Functions Objectives of this Section Evaluate Exponential Functions Graph Exponential Functions.
Q Exponential functions f (x) = a x are one-to-one functions. Q (from section 3.7) This means they each have an inverse function. Q We denote the inverse.
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.
Logarithms 2.5 Chapter 2 Exponents and Logarithms 2.5.1
Logarithmic Functions & Their Graphs
PRE-AP PRE-CALCULUS CHAPTER 3, SECTION 3 LOGARITHMIC FUNCTIONS AND THEIR GRAPHS
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.
Chapter 4 – Exponential and Logarithmic Functions Logarithmic Functions.
Lesson 3.2 Read: Pages Handout 1-49 (ODD), 55, 59, 63, 68, (ODD)
The Logarithm as Inverse Exponential Function Recall: If y is a one to one function of x, to find the inverse function reverse the x’s and y’s and solve.
4.1 – ONE-TO-ONE FUNCTIONS; INVERSE FUNCTIONS Target Goals: 1.Obtain the graph of the inverse function 2.Determine the inverse of a function.
4.4 Logarithmic Functions Morgan From his TV show, what is Dexter’s last name?
Review Exponential + Logarithmic Functions Math Analysis.
Math 1304 Calculus I 1.6 Inverse Functions. 1.6 Inverse functions Definition: A function f is said to be one-to- one if f(x) = f(y) implies x = y. It.
1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-1 Exponential and Logarithmic Functions Chapter 9.
Warm Up Find the VA, HA & intercepts: VA x = -3x = -2 HA y = 0y = 3 Intercepts (0,4/3)(1/3, 0) (0,-1/2)
8.4 Logarithmic Functions
6-2: Properties of Logarithms Unit 6: Exponents/Logarithms English Casbarro.
Math – Exponential Functions
Graphing Rational Expressions. Find the domain: Graph it:
LEQ: HOW DO YOU EVALUATE COMMON LOGARITHMS? Common Logarithms Sec. 9-5.
2.5.1 MATHPOWER TM 12, WESTERN EDITION 2.5 Chapter 2 Exponents and Logarithms.
Copyright © 2011 Pearson Education, Inc. Logarithmic Functions and Their Applications Section 4.2 Exponential and Logarithmic Functions.
Slide the Eraser 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
Logarithmic Functions
Logarithmic Functions and Their Graphs
6.1 One-to-One Functions; Inverse Function
Sullivan Algebra and Trigonometry: Section 6.3 Exponential Functions
Sullivan Algebra and Trigonometry: Section 6.3
College Algebra Chapter 4 Exponential and Logarithmic Functions
Section 3.5 Rational Functions and Their Graphs
One-to-One Functions and Inverse Functions
Logarithmic Functions and Their Graphs
Exponents and Logarithms
4.2 Exponential Functions
6.2 Exponential Functions
4.1 One-to-One Functions; Inverse Function
Sullivan Algebra and Trigonometry: Section 6.1
6.1 One-to-One Functions; Inverse Function
4.2 Exponential Functions
Inverse Functions and Logarithms.
{(1, 1), (2, 4), (3, 9), (4, 16)} one-to-one
6.3 Logarithms and Logarithmic Functions
Logarithmic Functions
Graphing Rational Expressions
Sullivan Algebra and Trigonometry: Section 6.2
Logarithmic Functions
Derivatives of Logarithmic and Exponential functions
Presentation transcript:

Sec

Write the expression using logs: 2 x =7.2

log 2 7.2=x

If every horizontal line intersects the graph of a function f at no more than one point, the f is a(n) ____________ function.

one-to-one

Find the inverse: f(x) = 2x + 6

Write the expression in exponential form: log 2 M = 1.3

2 1.3 = M

If the graph of every exponential function f(x) = a x, a>0, a not = 1, is decreasing, then a must be less than _________.

1

Graph f(x)=4 x

(0,1) (1,4) (-1,1/4)

If f -1 denotes the inverse of a function f, then the graphs of f and f -1 are symmetric with respect to the line ___________.

y = x

Find the inverse: {(1,2),(2,8),(3,18),(4,32)}

{(2,1),(8,2),(18,3),(32,4)}

Graph f(x)=log 4 x

(1,0) (4,1) (1/4,-1)

What is the asymptote of the graph f(x)=5+e -x ?

y = 5

Solve: (1/5) 2-x = 25

x = 4

What is the domain of the function f(x)=3 x+2 ?

What is the domain ?

Find the exact value (without using a calculator)

4

What is the domain of the function?

Determine if the two functions are inverses of each other:

no

Solve:

x = 2

What is the asymptote of the function h(x) = 3 + log(x + 2)?

x = -2

What is the domain of the function F(x) = log(2-x)?

Determine if the two functions are inverses of each other:

yes f(g(x)) = g(f(x)) =x