AP Calculus AB Chapter 3, Section 6 A Summary of Curve Sketching 2013 - 2014.

Slides:

Advertisements

Similar presentations

4.3 Derivatives and the shapes of graphs 4.4 Curve Sketching

Advertisements

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.

Basic Functions and Their Graphs

Copyright © Cengage Learning. All rights reserved. 12 Further Applications of the Derivative.

2.7 Graphs of Rational Functions. Steps of Graphing 1. Find the domain of the function 2. Simplify the function 3. Find and plot the y-intercept by evaluating.

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.

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

Section 3.6 – Curve Sketching. Guidelines for sketching a Curve The following checklist is intended as a guide to sketching a curve by hand without a.

2.7 – Graphs of Rational Functions. By then end of today you will learn about……. Rational Functions Transformations of the Reciprocal function Limits.

1 Sec 4.3 Curve Sketching. 2 Curve Sketching Problems Given: A function y = f(x). Objective: To sketch its graph.

Applications of Differentiation Curve Sketching. Why do we need this? The analysis of graphs involves looking at “interesting” points and intervals and.

How do I graph and use exponential growth and decay functions?

Rational Functions Objective: To graph rational functions without a calculator using what we have learned.

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.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 4.3 Connecting f ’ and f ” with the graph of f.

Calculus - Santowski 10/8/20151Calculus - Santowski.

Chapter 4 – Applications of Differentiation

Curve Sketching Lesson 5.4. Motivation Graphing calculators decrease the importance of curve sketching So why a lesson on curve sketching? A calculator.

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

Example Ex. Find all asymptotes of the curve Sol. So x=3 and x=-1 are vertical asymptotes. So y=x+2 is a slant asymptote.

AP CALCULUS AB Chapter 2: Limits and Continuity Section 2.2: Limits Involving Infinity.

Curve Sketching 2.7 Geometrical Application of Calculus

AP Calculus AB Chapter 3, Section 5 Limits at Infinitiy

Section 2.6 Rational Functions Part 1

AP Calculus AB Chapter 2, Section 5 Implicit Differentiation

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

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

MAT 1234 Calculus I Section 3.5/ 3.6 Graphing with Maple

What is the symmetry? f(x)= x 3 –x.

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.

Graphing Rational Functions Objective: To graph rational functions without a calculator.

Chapter Three: Section Six A summary of Curve Sketching.

Pre-AP Pre-Calculus Chapter 2, Section 6 Graphs of Rational Functions

Logarithms 2.5 Chapter 2 Exponents and Logarithms 2.5.1

PRE-AP PRE-CALCULUS CHAPTER 3, SECTION 3 LOGARITHMIC FUNCTIONS AND THEIR GRAPHS

A SUMMARY OF CURVE SKETCHING Section 3.6. When you are done with your homework, you should be able to… Analyze and sketch the graph of a function.

Section 3.5 Summary of Curve Sketching. THINGS TO CONSIDER BEFORE SKETCHING A CURVE Domain Intercepts Symmetry - even, odd, periodic. Asymptotes - vertical,

Copyright © 2015, 2008, 2011 Pearson Education, Inc. Section 4.3, Slide 1 Chapter 4 Exponential Functions.

Essential Question: How do you find intercepts, vertical asymptotes, horizontal asymptotes and holes? Students will write a summary describing the different.

 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.

In the past, one of the important uses of derivatives was as an aid in curve sketching. Even though we usually use a calculator or computer to draw complicated.

CALCULUS CHAPTER 3 SECTION 6: SUMMARY OF CURVE SKETCHING.

Notes Over 4.2 Sketching Graphs of a Rational Function Steps in Graphing a Rational Function. 1.Find the vertical and horizontal asymptotes of the function.

3.6 A Summary of Curve Sketching x-intercepts and y-intercepts (P.1) Symmetry(P.1) Domain and Range(P.3) Continuity(1.4) Vertical Asymptotes(1.5) Differentiability(2.1)

Math – Exponential Functions

Curve Sketching. Objective To analyze and sketch an accurate graph of a function. To analyze and sketch an accurate graph of a function.

Chapter 5 Graphing and Optimization Section 2 Second Derivative and Graphs (Part I)

Rational Functions Objective: To graph rational functions without a calculator using what we have learned.

Twenty Questions Rational Functions Twenty Questions

Section 2.6 Rational Functions Part 2

Analyzing Rational Functions

Relative Extrema and More Analysis of Functions

4.3 Derivatives and the shapes of graphs 4.5 Curve Sketching

Section 3.6 A Summary of Curve Sketching

AP Calculus AB Chapter 5, Section 1 ish

Curve Sketching Lesson 5.4.

Guidelines for sketching the graph of a function

Chapter 12 Graphing and Optimization

Infinite Limits Calculus 1-5.

Applications of the Derivative

Characteristics of Exponential Functions

Warm up Evaluate the expression without using a calculator. 1. 5–2 1

Section 6 – Critical Points and Extrema

AP Calculus BC September 28, 2016.

A SUMMARY OF CURVE SKETCHING

5. Curve Sketching.

Applications of the Derivative

- Derivatives and the shapes of graphs - Curve Sketching

Chapter 4 Graphing and Optimization

Presentation transcript:

AP Calculus AB Chapter 3, Section 6 A Summary of Curve Sketching

Analyzing graphs Here are some concepts you have studied that determine how a graph looks: – X-intercepts and y-intercepts – Symmetry – Domain & range – Continuity – Vertical asymptotes – Differentiability – Relative extrema – Concavity – Points of inflection – Horizontal asymptotes – Infinite limits at infinity

What is an appropriate viewing window?

Without using a calculator, see if you can sketch the graph of the function by analyzing it using the different ways listed on the first slide.

Ch. 3.6 Homework Pg 215 – 217, #’s: 1 – 5, 15, 27, 57, 75 9 total problems