Exponential Functions Karen Kelley East Garner Magnet Middle School Common Core Math 2.

Slides:



Advertisements
Similar presentations
Logarithmic Functions.
Advertisements

Graphs of Exponential and Logarithmic Functions
Warm Up Section 3.6B (1). Show that f(x) = 3x + 5 and g(x) = are inverses. (2). Find the inverse of h(x) = 8 – 3x. (3). Solve: 27 x – 1 < 9 2x + 3 (4).
3.6 Graph Rational Functions Part II. Remember Rational functions have asymptotes To find the vertical asymptote, set the denominator = 0 and solve for.
EXAMPLE 1 Find an inverse relation Find an equation for the inverse of the relation y = 3x – 5. Write original relation. y = 3x – 5 Switch x and y. x =
Date: Lesson 8.1. I can graph exponential growth functions; graph exponential decay functions. Common Core: CC.9-12.F.IF.7e CRS: FUN 501.
How does one Graph an Exponential Equation?
Logarithmic Functions
1) log416 = 2 is the logarithmic form of 4░ = 16
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.
Warm Up Section 3.6B (1). Show that f(x) = 3x + 5 and g(x) =
Logarithmic Functions. y = log a x if and only if x = a y The logarithmic function to the base a, where a > 0 and a  1 is defined: exponential form logarithmic.
UNIT 4: “POWER TRIP” Standard 4.1: demonstrate understanding of the properties of exponents and to graph exponential functions (11-1, 11-2) Standard.
Unit 6: Modeling Mathematics 3 Ms. C. Taylor. Warm-Up.
Aim: What is an exponential function?
3.2 Day 2 Logarithmic Functions –Graph logarithmic functions. –Find the domain of a logarithmic function. Pg. 397 # 44, 46, even, 76, 78 For #54-58.
Logarithms.
Logarithmic Functions. y = log a x if and only if x = a y The logarithmic function to the base a, where a > 0 and a  1 is defined: exponential form logarithmic.
Jeopardy Inverses Geometric Sequences Exponential Functions Rational Exponents Random Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q.
Chapter 7.1 Common Core – N.RN.1 & N.RN.2 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer.
Warm-up Solve: log3(x+3) + log32 = 2 log32(x+3) = 2 log3 2x + 6 = 2
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.
Rational Exponents and Radical Functions
A rational function is a function whose rule can be written as a ratio of two polynomials. The parent rational function is f(x) = . Its graph is a.
What is the symmetry? f(x)= x 3 –x.
1 Factoring Practice (5 questions). 2 Factoring Practice (Answers)
8-2: Exponential Decay Objective Ca Standard 12: Students know the laws of fractional exponents, understand exponential functions and use these functions.
Warm-up 12/14/12 1.Solve the system by any method 2.Set up the system of equations A math test is to have 20 questions. The test format uses multiple choice.
Logarithms 2.5 Chapter 2 Exponents and Logarithms 2.5.1
Section 4.4 Logarithmic Functions. Definition:Definition: 2) A logarithm is merely a name for a certain exponent! 2) A logarithm is merely a name for.
5.4 Logarithmic Functions. Quiz What’s the domain of f(x) = log x?
The inverse function of an Exponential functions is a log function. The inverse function of an Exponential functions is a log function. Domain: Range:
Exploring Exponential Functions Using a Graphing Calculator.
Exponential & Logarithmic functions. Exponential Functions y= a x ; 1 ≠ a > 0,that’s a is a positive fraction or a number greater than 1 Case(1): a >
GRAPHING EXPONENTIAL FUNCTIONS f(x) = 2 x 2 > 1 exponential growth 2 24–2 4 6 –4 y x Notice the asymptote: y = 0 Domain: All real, Range: y > 0.
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.
Math 71B 9.3 – Logarithmic Functions 1. One-to-one functions have inverses. Let’s define the inverse of the exponential function. 2.
GPS: MM3A2c, MM3A2e, MM3A2f.  MM3A2c – Define logarithmic functions as inverses of exponential functions.  MM3A2f – Graph functions as transformations.
Unit 3 Day 10 – Transformations of Logarithmic Functions.
(a) (b) (c) (d) Warm Up: Show YOUR work!. Warm Up.
Exponential & Logarithmic functions. Exponential Functions y= a x ; 1 ≠ a > 0,that’s a is a positive fraction or a number greater than 1 Case(1): a >
3.2 Logarithmic Functions and Their Graphs We know that if a function passes the horizontal line test, then the inverse of the function is also a function.
Math – Exponential Functions
Logarithmic Functions. y = log a x if and only if x = a y The logarithmic function to the base a, where a > 0 and a  1 is defined: exponential form logarithmic.
INVERSE Logarithmic and Exponential Graphs and Graphing.
Chapter 7.1 Common Core – N.RN.1 & N.RN.2 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer.
MGSE9-12.A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
LEQ: HOW DO YOU EVALUATE COMMON LOGARITHMS? Common Logarithms Sec. 9-5.
Warm Up Evaluate the following. 1. f(x) = 2 x when x = f(x) = log x when x = f(x) = 3.78 x when x = f(x) = ln x when x =
2.5.1 MATHPOWER TM 12, WESTERN EDITION 2.5 Chapter 2 Exponents and Logarithms.
Logarithmic Functions & Their Graphs Goals— Recognize and evaluate logarithmic functions with base a Graph Logarithmic functions Recognize, evaluate, and.
A rational function is a function whose rule can be written as a ratio of two polynomials. The parent rational function is f(x) = . Its graph is a.
Warmup 3-24 Simplify. Show work! Solve for x. Show work! 4. 5.
1. Given the equation y = 650(1.075)x
Solve the radical equation
How does one Graph an Exponential Equation?
Warmup Let f(x) = x – 3 and g(x) = x2. What is (f ○ g)(1)?
Common Logs and Applications
Exponential Functions
MATH 1310 Section 5.1.
Graphing Exponential Functions Exponential Growth p 635
Exponential Functions
Graph rational functions.
6.9 Graphing Exponential Equations
In symbol, we write this as
MATH 1310 Section 5.1.
7.4 Graphing Exponential Equations
MATH 1310 Section 5.1.
15 – Transformations of Functions Calculator Required
Exponential Functions and Their Graphs
Presentation transcript:

Exponential Functions Karen Kelley East Garner Magnet Middle School Common Core Math 2

Expected Outcomes: Participants will gain an understanding of... The vertical alignment of CCM1, CCM2, and CCM3 the changes made to C-MAPP in general. the Common Core Math 2 Exponential Functions unit. how to use the Core-Plus Mathematics materials. how to use mathematical stations in the math classroom. the importance of mathematical discourse.

CCM1CCM2CCM3 Properties of Exponents – Integers and some Rational Properties of Exponents – More Rational Exponential Growth and Decay taught separately Review of Exponential Functions – all together Exponential and Logarithmic Functions Translations – f(x) + k, f(x + k), and f(x + h) + k Transformations - f(x) + k, f(x + k), f(x + h) + k, k(f(x)), f(kx), etc. Key Features: Domain, Range, End Behavior Key Features: Domain, Range, End Behavior, Asymptotes, Practical Domain Inverse Functions – reflection over y = x and switch x and y values before solving for y. Inverse Functions - reflection over y = x, switch x and y values before solving for y, inverse notation, composition Common Logarithms – no other bases, no change of base All other logarithms – properties of logarithms, other bases, change of base Arithmetic vs Geometric Sequences Sequences and Series

The New Face of C-MAPP Unit Guides – those hidden features Excel Spreadsheet for pacing and resources Warm-ups Assessments: Pre-Assessment, Formative Assessments, Summative Assessments Lesson Folders – with answer keys!! Let’s take a closer look!!

CCM2: Exponential Functions This C-MAPP unit has been divided into 5 main parts: Rational Exponents & Radicals Review of Exponential Functions – what we already know and Point-Ratio Form Transformation of Graphs – vertical, horizontal transformations, and more Inverse Functions Common Logarithms Let’s take a look!

Inverse Function Stations Implementation Ideas – to move or not to move Preparation Explicit Directions Debrief

Break Time!!

Common Logarithms Core-Plus Mathematics Lesson: Lesson Launch Think About It Investigation Summarize the Mathematics Check for Understanding

It’s a wrap... GREAT JOB EVERYONE... later this week you’ll be using what you’ve learned in your PLT groups as you prepare for the upcoming school year.