4.4 Graph Exponential Growth Functions

Slides:



Advertisements
Similar presentations
Growth and Decay Exponential Models. Differs from polynomial functions. Polynomial Functions have exponents of whole numbers Exponential Functions have.
Advertisements

Graph of Exponential Functions
Objectives: 1.Be able to graph the exponential growth parent function. 2.Be able to graph all forms of the exponential growth function Critical Vocabulary:
Graphing Exponential Functions What you need to know… To find the y-intercept of an exponential function, evaluate f(0). The y-intercept has the coordinates.
Intercepts, Exponentials, and Asymptotes Section 3.4 Standard: MCC9-12.F.IF.7a&e Essential Question: How do you graph and analyze exponential functions.
EXAMPLE 4 Classify and write rules for functions SOLUTION The graph represents exponential growth (y = ab x where b > 1). The y- intercept is 10, so a.
Exponential Growth and Exponential Decay
8.1 Exponential Growth Goal: Graph exponential growth functions.
8.2 Exponential Decay P Exponential Decay Has the same form as growth functions f(x) = ab x Where a > 0 BUT: 0 < b < 1 (a fraction between 0 & 1)
Exponential Growth and Decay Functions. What is an exponential function? An exponential function has the form: y = ab x Where a is NOT equal to 0 and.
Objective: Students will be able to write and evaluate exponential expressions to model growth and decay situations.
Tuesday April 15, Exponential Growth Functions
How does one Graph an Exponential Equation?
Negative Exponents Fraction Exponent Graphs Exponential function Misc
The Natural Base e Section 6.2 beginning on page 304.
10.2: Infinite Limits. Infinite Limits When the limit of f(x) does not exist and f(x) goes to positive infinity or negative infinity, then we can call.
How do I graph and use exponential growth and decay functions?
8-1 Exploring Exponent Models Objectives:  To identify exponential growth and decay.  To define the asymptote  To graph exponential functions  To find.
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 7.1: Graph Exponential Growth Functions Chapter 7: Exponential and Logarithmic Functions.
Evaluate each expression for the given value of x.
Graphing Exponentials and Logs
2.2 Limits Involving Infinity Goals: Use a table to find limits to infinity, use the sandwich theorem, use graphs to determine limits to infinity, find.
Do Now: Explain what an asymptote is in your own words.
Graph Exponential Growth Functions 4.4 (M2) Quiz: Friday Computer Lab (C28): Monday **You need graph paper**
Objective: TSW graph exponential functions and identify the domain and range of the function.
State the domain and range of each function Exponential Growth and Decay.
8-2 Properties of Exponential Functions. The function f(x) = b x is the parent of a family of exponential functions for each value of b. The factor a.
8-2: Exponential Decay Objective Ca Standard 12: Students know the laws of fractional exponents, understand exponential functions and use these functions.
Algebra II w/ trig. Exponential Functions – has the form y= ab x, where a ≠0, b>0, and b≠1 - y represents the quantity after time is expired - a represents.
Exponential Graphs Equations where the variable (x) is the POWER y = ab x – h + k h moves the graph horizontally k moves the graph vertically.
Rational Functions and Asymptotes
Intro to Graphing Exponentials Mon Oct 22 nd / Tue Oct 23 rd.
Notes Over 8.2 Recognizing Exponential Growth and Decay Exponential Growth Model Exponential Decay Model.
Exploring Exponential Functions Using a Graphing Calculator.
TODAY IN ALGEBRA 2.0…  REVIEW: Solving Exponential Equations  Learning Target 1: 7.6 You will solve exponential equations by using logarithms  Independent.
Graphing Exponential Growth and Decay. An exponential function has the form b is a positive number other than 1. If b is greater than 1 Is called an exponential.
Graphing Exponential function parent function: y = 2 x X is the exponent!!! What does this look like on a graph? In the parent function the horizontal.
8-1: Exponential Growth Objective CA 12: Students know the laws of fractional exponents, understanding exponential functions, and use these functions in.
Ch. 4.4 to 4.5. “a” changes the steepness of the growth or decay If (-a) graph is flipped “b” is the base it determines if it is an EXPONENTIAL GROWTH.
Determine the value of the unknown. 5 min. WHAT DO EXPONENTIAL FUNCTIONS LOOK LIKE? Sec
8.5 and 8.6 Writing and Graphing Exponential Growth and Decay Functions Students will learn to Write exponential growth and decay functions Graph exponential.
Chapter 8-2 Properties of Exponential Functions
Exponential Functions An exponential function is represented: F(x) = a b x a = starting amount (when x = 0) b = base that is multiplied. b must be greater.
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.
TODAY IN ALGEBRA 2.0…  REVIEW: HW #3 Exponential Growth and Decay  Learning Target 1: 7.4 You will evaluate logarithms.  Independent Practice.
How do I graph and use exponential growth and decay functions?
8.1 Exponential Growth 8.2 Exponential Decay. Exponential Function An exponential function has a positive base other than 1. The general exponential function.
Do Now: State the domain of the function.. Academy Algebra II 7.1, 7.2: Graph Exponential Growth and Decay Functions HW: p.482 (6, 10, even), p.489.
Exponential Functions 4.3 **You might want graph paper**
Graph Y-Intercept =(0,2) Horizontal Asymptote X-Axis (y = 0) Domain: All Real Numbers Range: y > 0.
8.1 & 8.2 Exponential Functions 3/10/2014. In this lesson we will learn … What an exponential function is. Difference between exponential growth and decay.
Lesson 8.1.  Exponential Function: a function that involves the expression b x where the base b is a positive number other than 1.  Asymptote: a line.
Calculus Sections 5.1 Apply exponential functions An exponential function takes the form y = a∙b x where b is the base and b>0 and b≠1. Identify as exponential.
8-3: The Number ‘e’ (Day 1) Objective (Ca. Standard 12): Students know the laws of fractional exponents, understand exponential function, and use these.
Warm-up , a) 8000 b)32, a) 6975 b)62, ,390, mg, 27.3 mg Homework Solutions.
Over Lesson 7–4 5-Minute Check 1 A.3.3 × 10 4 B × 10 4 C × 10 6 D × 10 7 What is 3,352,000 in scientific notation?
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.
8.1 & 8.2 Exponential Growth and Decay 4/16/2012.
How does one Graph an Exponential Equation?
Using Functions Involving e
Warm up Evaluate the expression without using a calculator. 1. 5–2 1
Characteristics OF EXPONENTIAL FUNCTIONS!!!!!.
Unit 3 Day 10 – Transformations of Logarithmic Functions
Exponential Functions: Differentiation and Integration
Limits at Infinity Calculus 3-5.
6.9 Graphing Exponential Equations
7.4 Graphing Exponential Equations
Today in Pre-Calculus Go over homework.
Presentation transcript:

4.4 Graph Exponential Growth Functions

Vocabulary Exponential Function: y = abx, where a ≠ 0 and the base b is a positive number other than 1. Examples:

Exponential Growth & Decay y = abx

Vocabulary asymptote: line that the graph approaches more and more closely, but does not touch or cross

Vocabulary end behavior of a function’s graph: the y-behavior of the graph as x approaches positive or negative infinity.

Graphing y = bx Graph y = 4x X Y -2 -1 1 2

Graphing y = abx Graph X Y -1 1

Graphing y = abx Graph X Y 1 2

Graphing y = abx-h+k Translates the graph left 2 units down 1 unit

Graphing y = abx-h+k Graph

Classwork p. 121 #’s 1-3 (graph the functions)

Homework Pg. 122, 1 – 17 all