Graphing Linear Equations: Warm Up: Brainstorm what you know about Graphing Lines: (Try to fill the whole page) Graphing
|
|
- Laureen Reeves
- 5 years ago
- Views:
Transcription
1
2 Graphing Linear Equations: Warm Up: Brainstorm what you know about Graphing Lines: (Try to fill the whole page) Graphing
3 Notes: The three types of ways to graph a line and when to use each: Slope intercept form: Intercept Method: XY chrt (table of values): Graph the following lines: x + y = 3 2x + 3y = 12
4 x 3 y 1 x = -3 Y = 4 y = x y x 3 Points to Remember: Homework:
5 Writing the Equation of a Line: Warm-up: Solve each equation for Y, then find the slope of the line. A. 3x + 4y = 7 B. -2x 6y = 2 Graph each equation A. y = ½ x + 3 B. 2x 3y = 12 Write the equation of the line given: A. Slope of 3 and a y intercept of -2 B. m = -5 and b = 7 Notes: What do I need to write the equation of a line:
6 Forms to write the equation of a line: Slope intercept: Point Slope: Standard Form: Find an equation in standard form for each line: 1. through (-3, 5) (-6,4) Using Slope intercept form: Using point slope form: Find the equation in standard form : 1. Through the point (4,-3) and has a slope of Using slope intercept form: 2 5 Using point slope form:
7 2. Having a slope of -2 and a y intercept of 3 4. Using slope intercept form: Using point slope form: 3. Passing through the points: Using slope intercept form: 3, 4 5 4, 1 1, 4 2 Using point slope form: Points to Remember: Homework: Page eoo.
8 Mathematician: Extra Credit Use the following information to help with some of the problems. Standard form of an equation is AX + BY = C. The slope of the line is then. Find the value of K so that it has the given slope m. 1. kx 3 y = 7, m = x + ky = 10, m = 2 3. (k+3)x 3y = 1 m = k 4. (k+1)x + 2y = 6, m = k-2 Find the value of K so that the line through the given point has the slope m. **Hint** think about what formula you need. 5. (2k,3) (1,k) m = 2 6. (k+1, 3+2k) (k-1, 1-k) m = k
9 Functions and Slope Warm Up: Find the slope of the line: (4,1) (8,7) Write the general form of the following: Point Slope Form: Slope Intercept Form: Write the equation of the line in slope intercept form given the following information: m = 2 b = 3 Point (0,1) Slope = -1 Point ( 1, 5) Slope = 2 Point (6, -2) Slope 3 2 What does the acronym AKA mean?
10 Notes: Notation: Slope intercept form is. Another way to write it is in function form. Therefore y is the same as. The part in the parenthesis is the. Also it is equal to. f(-4) = 8 can be written as because f( ¾ ) = -5 can be written as - Find an equation of the linear function f using the given information. 1. m = 2, b = 3 2. m = -1 b = ½ 3. m=2 and f(1) = 5 4. m = 3, f(0) = 1
11 5. f (3) = 4, f(6) = f(-1) = 2, f(2) = 2 Points to Remember: Homework: page 149 written exercises 1-21 odd
12 Functions and Relations Warm Up: Find the slope of the line and write the equation of the line: A. f(-2) = 5, f(-2) = 12 B. f(3) = 8, f(4) = 8 C. f(0) = 2, f(6) =18 Write the definition of domain: Write the definition of range: Give the range of the equation 4-2x for the domain { -1, 0, 1, 2, 3} If f(x) = 2x + 5 find f(3)
13 NOTES: Definition of Relation: Function: How a relation can be a function: State the domain and range of the relation. Is the relation a function? {(-1, 2), (0,1), (1,2)} {(2,1), (1,-1), (0.2) (2,0)} Domain: Range: Function yes or no and why: Domain: Range: Function yes or no and why: Domain: Range: Function yes or no and why: Domain: Range: Function yes or no and why:
14 More new notation: Old Notation: Semi New Notation Very New Notation Y = 2x f(x) = 2s f : x 2x y = -3x + 5 g(x) = -3x +5 g : x 3x 5 Analysis: Find the range for each function: What does that mean? What do we do? 2 f : x 1 x D = { -1, 0,1 } 2 3 H : z z z D = {-1,0,1,2} How do I do this on the calculator: Points to Remember: Homework: Page odd by hand show all work odd on the graphing calculator. Page 155 oral exercises 1-9 odd page 156 written exercises 1-5 odd. Just tell if relation is a function why or why not.
15 Functions and Relations Continued Warm Up: Write the equation of the line give the following conditions: A. f(0) = -1; f(x) decreases by 3 when x increases by 1. B. f(3) = 7 and f(-5) = 7 C. f(3) = 4 and f(6) = -3 Explain how you know a relation is a function: Is the relation a function, why or why not? A. {(1,2),(2,2),(3,1),(4,1)} B.
16 NOTES: Definition of Domain: What is the domain of a square root function: We know that you can not take the square root of a ; so the doma2in has to be. Therefore anything inside the AKA must be zero. We also know that we can NOT by zero. Which means the of a fraction can not equal. Therefore the domain of a fraction is real numbers where the denominator would be to. Give the domain of each function 2 g ( x ) f ( x ) 2x 1 x 3 g ( x ) ( x 2 1)( x 2) Points to Remember: Homework:
Math M111: Lecture Notes For Chapter 3
Section 3.1: Math M111: Lecture Notes For Chapter 3 Note: Make sure you already printed the graphing papers Plotting Points, Quadrant s signs, x-intercepts and y-intercepts Example 1: Plot the following
More informationSB CH 2 answers.notebook. November 05, Warm Up. Oct 8 10:36 AM. Oct 5 2:22 PM. Oct 8 9:22 AM. Oct 8 9:19 AM. Oct 8 9:26 AM.
Warm Up Oct 8 10:36 AM Oct 5 2:22 PM Linear Function Qualities Oct 8 9:22 AM Oct 8 9:19 AM Quadratic Function Qualities Oct 8 9:26 AM Oct 8 9:25 AM 1 Oct 8 9:28 AM Oct 8 9:25 AM Given vertex (-1,4) and
More informationFunctions & Graphs. Section 1.2
Functions & Graphs Section 1.2 What you will remember Functions Domains and Ranges Viewing and Interpreting Graphs Even Functions and Odd Functions Symmetry Functions Defined in Pieces Absolute Value Functions
More informationHomework 6. (x 3) 2 + (y 1) 2 = 25. (x 5) 2 + (y + 2) 2 = 49
245 245 Name: Solutions Due Date: Monday May 16th. Homework 6 Directions: Show all work to receive full credit. Solutions always include the work and problems with no work and only answers will receive
More informationSolve the problem. Determine the center and radius of the circle. Use the given information about a circle to find its equation.
Math1314-TestReview2-Spring2016 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) Is the point (-5, -3) on the circle defined
More informationLinear Equations. Find the domain and the range of the following set. {(4,5), (7,8), (-1,3), (3,3), (2,-3)}
Linear Equations Domain and Range Domain refers to the set of possible values of the x-component of a point in the form (x,y). Range refers to the set of possible values of the y-component of a point in
More informationGeorgia Department of Education Common Core Georgia Performance Standards Framework CCGPS Advanced Algebra Unit 2
Polynomials Patterns Task 1. To get an idea of what polynomial functions look like, we can graph the first through fifth degree polynomials with leading coefficients of 1. For each polynomial function,
More informationUnit 4 Day 4 & 5. Piecewise Functions
Unit 4 Day 4 & 5 Piecewise Functions Warm Up 1. Why does the inverse variation have a vertical asymptote? 2. Graph. Find the asymptotes. Write the domain and range using interval notation. a. b. f(x)=
More informationGUIDED NOTES 5.6 RATIONAL FUNCTIONS
GUIDED NOTES 5.6 RATIONAL FUNCTIONS LEARNING OBJECTIVES In this section, you will: Use arrow notation. Solve applied problems involving rational functions. Find the domains of rational functions. Identify
More informationGeometry/Trig Name: Date: Lesson 1-11 Writing the Equation of a Perpendicular Bisector
Name: Date: Lesson 1-11 Writing the Equation of a Perpendicular Bisector Learning Goals: #14: How do I write the equation of a perpendicular bisector? Warm-up What is the equation of a line that passes
More informationTwitter: @Owen134866 www.mathsfreeresourcelibrary.com Prior Knowledge Check 1) Simplify: a) 3x 2 5x 5 b) 5x3 y 2 15x 7 2) Factorise: a) x 2 2x 24 b) 3x 2 17x + 20 15x 2 y 3 3) Use long division to calculate:
More informationSolving Equations Quick Reference
Solving Equations Quick Reference Integer Rules Addition: If the signs are the same, add the numbers and keep the sign. If the signs are different, subtract the numbers and keep the sign of the number
More information( ) is called the dependent variable because its
page 1 of 16 CLASS NOTES: 3 8 thru 4 3 and 11 7 Functions, Exponents and Polynomials 3 8: Function Notation A function is a correspondence between two sets, the domain (x) and the range (y). An example
More informationFunction Junction: Homework Examples from ACE
Function Junction: Homework Examples from ACE Investigation 1: The Families of Functions, ACE #5, #10 Investigation 2: Arithmetic and Geometric Sequences, ACE #4, #17 Investigation 3: Transforming Graphs,
More informationChapter 2 notes from powerpoints
Chapter 2 notes from powerpoints Synthetic division and basic definitions Sections 1 and 2 Definition of a Polynomial Function: Let n be a nonnegative integer and let a n, a n-1,, a 2, a 1, a 0 be real
More information6-6 Solving Systems of Linear Inequalities 6-6. Solving Systems of Linear Inequalities
6-6 Solving Systems of Linear Inequalities Warm Up Lesson Presentation Lesson Quiz 1 2 pts 3 pts 5 pts Bell Quiz 6-6 Solve each inequality for y. 1. 8x + y < 6 2. 3x 2y > 10 3. Graph the solutions of 4x
More information6-4 Solving Special Systems
6-4 Solving Special Systems Warm Up Lesson Presentation Lesson Quiz 1 2 pts Bell Quiz 6-4 Solve the equation. 1. 2(x + 1) = 2x + 2 3 pts Solve by using any method. 2. y = 3x + 2 2x + y = 7 5 pts possible
More informationb) since the remainder is 0 I need to factor the numerator. Synthetic division tells me this is true
Section 5.2 solutions #1-10: a) Perform the division using synthetic division. b) if the remainder is 0 use the result to completely factor the dividend (this is the numerator or the polynomial to the
More informationChapter 3: Inequalities, Lines and Circles, Introduction to Functions
QUIZ AND TEST INFORMATION: The material in this chapter is on Quiz 3 and Exam 2. You should complete at least one attempt of Quiz 3 before taking Exam 2. This material is also on the final exam and used
More informationAlgebra I - Study Guide for Final
Name: Date: Period: Algebra I - Study Guide for Final Multiple Choice Identify the choice that best completes the statement or answers the question. To truly study for this final, EXPLAIN why the answer
More information2. If the discriminant of a quadratic equation is zero, then there (A) are 2 imaginary roots (B) is 1 rational root
Academic Algebra II 1 st Semester Exam Mr. Pleacher Name I. Multiple Choice 1. Which is the solution of x 1 3x + 7? (A) x -4 (B) x 4 (C) x -4 (D) x 4. If the discriminant of a quadratic equation is zero,
More informationAlgebra 2 and Trigonometry
Algebra 2 and Trigonometry Chapter 7: Exponential Functions Name: Teacher: Pd: 1 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs.
More informationL Hopital s Rule. We will use our knowledge of derivatives in order to evaluate limits that produce indeterminate forms.
L Hopital s Rule We will use our knowledge of derivatives in order to evaluate its that produce indeterminate forms. Main Idea x c f x g x If, when taking the it as x c, you get an INDETERMINATE FORM..
More informationICM ~ Unit 4 ~ Day 3. Horizontal Asymptotes, End Behavior
ICM ~ Unit 4 ~ Day 3 Horizontal Asymptotes, End Behavior Warm Up ~ Day 3 1. Find the domain, then convert to fractional/rational eponent. f ( ) 7. Simplify completely: 3( + 5). 3. Find the domain, & y
More informationCalculus I Sample Exam #01
Calculus I Sample Exam #01 1. Sketch the graph of the function and define the domain and range. 1 a) f( x) 3 b) g( x) x 1 x c) hx ( ) x x 1 5x6 d) jx ( ) x x x 3 6 . Evaluate the following. a) 5 sin 6
More informationCHAPTER 1: Functions
CHAPTER : Functions SECTION.: FUNCTIONS (Answers for Chapter : Functions) A.. f x 2) f x 3) = x = x 4) Input x Output f x 3 0 4 5 2 6 5 5 + 4 π π + 4 0/3 22/3 4.7 8.7 c c + 4 a + h a + h + 4 Input x Output
More informationMath 3C Midterm 1 Study Guide
Math 3C Midterm 1 Study Guide October 23, 2014 Acknowledgement I want to say thanks to Mark Kempton for letting me update this study guide for my class. General Information: The test will be held Thursday,
More informationExample: f(x) = 2x² + 1 Solution: Math 2 VM Part 5 Quadratic Functions April 25, 2017
Math 2 Variable Manipulation Part 5 Quadratic Functions MATH 1 REVIEW THE CONCEPT OF FUNCTIONS The concept of a function is both a different way of thinking about equations and a different way of notating
More informationCHAPTER 2: Polynomial and Rational Functions
1) (Answers for Chapter 2: Polynomial and Rational Functions) A.2.1 CHAPTER 2: Polynomial and Rational Functions SECTION 2.1: QUADRATIC FUNCTIONS (AND PARABOLAS) ( ) ; c) x = 1 ( ) ( ) and ( 4, 0) ( )
More informationSOLUTIONS FOR PROBLEMS 1-30
. Answer: 5 Evaluate x x + 9 for x SOLUTIONS FOR PROBLEMS - 0 When substituting x in x be sure to do the exponent before the multiplication by to get (). + 9 5 + When multiplying ( ) so that ( 7) ( ).
More information2-7 Solving Quadratic Inequalities. ax 2 + bx + c > 0 (a 0)
Quadratic Inequalities In One Variable LOOKS LIKE a quadratic equation but Doesn t have an equal sign (=) Has an inequality sign (>,
More informationHerndon High School Geometry Honors Summer Assignment
Welcome to Geometry! This summer packet is for all students enrolled in Geometry Honors at Herndon High School for Fall 07. The packet contains prerequisite skills that you will need to be successful in
More informationUnit 1: Polynomial Functions SuggestedTime:14 hours
Unit 1: Polynomial Functions SuggestedTime:14 hours (Chapter 3 of the text) Prerequisite Skills Do the following: #1,3,4,5, 6a)c)d)f), 7a)b)c),8a)b), 9 Polynomial Functions A polynomial function is an
More informationHonors Advanced Algebra Unit 3: Polynomial Functions November 9, 2016 Task 11: Characteristics of Polynomial Functions
Honors Advanced Algebra Name Unit 3: Polynomial Functions November 9, 2016 Task 11: Characteristics of Polynomial Functions MGSE9 12.F.IF.7 Graph functions expressed symbolically and show key features
More information1 Lecture 25: Extreme values
1 Lecture 25: Extreme values 1.1 Outline Absolute maximum and minimum. Existence on closed, bounded intervals. Local extrema, critical points, Fermat s theorem Extreme values on a closed interval Rolle
More informationMAC College Algebra
MAC 05 - College Algebra Name Review for Test 2 - Chapter 2 Date MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the exact distance between the
More informationS4 (4.3) Quadratic Functions.notebook February 06, 2018
Daily Practice 2.11.2017 Q1. Multiply out and simplify 3g - 5(2g + 4) Q2. Simplify Q3. Write with a rational denominator Today we will be learning about quadratic functions and their graphs. Q4. State
More informationPre Calculus with Mrs. Bluell
Welcome to Pre Calculus with Mrs. Bluell Quick Review Today's Topics include Interval Notation Exponent Rules Quadrants Distance Formula Midpoint Formula Circle Formula Alligator Mouths to Interval Notation
More informationReview 1. 1 Relations and Functions. Review Problems
Review 1 1 Relations and Functions Objectives Relations; represent a relation by coordinate pairs, mappings and equations; functions; evaluate a function; domain and range; operations of functions. Skills
More informationAlgebra II (Common Core) Summer Assignment Due: September 11, 2017 (First full day of classes) Ms. Vella
1 Algebra II (Common Core) Summer Assignment Due: September 11, 2017 (First full day of classes) Ms. Vella In this summer assignment, you will be reviewing important topics from Algebra I that are crucial
More informationAlgebra 2 Summer Work Packet Review and Study Guide
Algebra Summer Work Packet Review and Study Guide This study guide is designed to accompany the Algebra Summer Work Packet. Its purpose is to offer a review of the nine specific concepts covered in the
More informationDetermine whether the formula determines y as a function of x. If not, explain. Is there a way to look at a graph and determine if it's a function?
1.2 Functions and Their Properties Name: Objectives: Students will be able to represent functions numerically, algebraically, and graphically, determine the domain and range for functions, and analyze
More informationUnit 9: Quadratics Intercept Form
For Teacher Use Packet Score: Name: Period: Algebra 1 Unit 9: Quadratics Intercept Form Note & Homework Packet Date Topic/Assignment HW Page 9-A Graphing Parabolas in Intercept Form 9-B Solve Quadratic
More informationHomework 1. 3x 12, 61.P (x) = 3t 21 Section 1.2
Section 1.1 Homework 1 (34, 36) Determine whether the equation defines y as a function of x. 34. x + h 2 = 1, 36. y = 3x 1 x + 2. (40, 44) Find the following for each function: (a) f(0) (b) f(1) (c) f(
More informationPolynomial Review Problems
Polynomial Review Problems 1. Find polynomial function formulas that could fit each of these graphs. Remember that you will need to determine the value of the leading coefficient. The point (0,-3) is on
More information1,3. f x x f x x. Lim. Lim. Lim. Lim Lim. y 13x b b 10 b So the equation of the tangent line is y 13x
1.5 Topics: The Derivative lutions 1. Use the limit definition of derivative (the one with x in it) to find f x given f x 4x 5x 6 4 x x 5 x x 6 4x 5x 6 f x x f x f x x0 x x0 x xx x x x x x 4 5 6 4 5 6
More information(a) Write down the value of q and of r. (2) Write down the equation of the axis of symmetry. (1) (c) Find the value of p. (3) (Total 6 marks)
1. Let f(x) = p(x q)(x r). Part of the graph of f is shown below. The graph passes through the points ( 2, 0), (0, 4) and (4, 0). (a) Write down the value of q and of r. (b) Write down the equation of
More informationV. Graph Sketching and Max-Min Problems
V. Graph Sketching and Max-Min Problems The signs of the first and second derivatives of a function tell us something about the shape of its graph. In this chapter we learn how to find that information.
More information3 Polynomial and Rational Functions
3 Polynomial and Rational Functions 3.1 Polynomial Functions and their Graphs So far, we have learned how to graph polynomials of degree 0, 1, and. Degree 0 polynomial functions are things like f(x) =,
More information8-1 Factors and Greatest Common Factors 8-1. Factors and Greatest Common Factors
8-1 Factors and Greatest Common Factors Warm Up Lesson Presentation Lesson Quiz 1 2 pts 2 pts Bell Quiz 8-1 Tell whether the second number is a factor of the first number 1. 50, 6 2 pts no 2. 105, 7 3.
More informationA Library of Functions
LibraryofFunctions.nb 1 A Library of Functions Any study of calculus must start with the study of functions. Functions are fundamental to mathematics. In its everyday use the word function conveys to us
More informationMath 155 Prerequisite Review Handout
Math 155 Prerequisite Review Handout August 23, 2010 Contents 1 Basic Mathematical Operations 2 1.1 Examples...................................... 2 1.2 Exercises.......................................
More informationQuarter 2 400, , , , , , ,000 50,000
Algebra 2 Quarter 2 Quadratic Functions Introduction to Polynomial Functions Hybrid Electric Vehicles Since 1999, there has been a growing trend in the sales of hybrid electric vehicles. These data show
More informationGUIDED NOTES 2.2 LINEAR EQUATIONS IN ONE VARIABLE
GUIDED NOTES 2.2 LINEAR EQUATIONS IN ONE VARIABLE LEARNING OBJECTIVES In this section, you will: Solve equations in one variable algebraically. Solve a rational equation. Find a linear equation. Given
More informationMHF4U. Advanced Functions Grade 12 University Mitchell District High School. Unit 3 Rational Functions & Equations 6 Video Lessons
MHF4U Advanced Functions Grade 12 University Mitchell District High School Unit 3 Rational Functions & Equations 6 Video Lessons Allow no more than 15 class days for this unit! This includes time for review
More informationSubtract 6 to both sides Divide by 2 on both sides. Cross Multiply. Answer: x = -9
Subtract 6 to both sides Divide by 2 on both sides Answer: x = -9 Cross Multiply. = 3 Distribute 2 to parenthesis Combine like terms Subtract 4x to both sides Subtract 10 from both sides x = -20 Subtract
More informationSolving a Linear-Quadratic System
CC-18 Solving LinearQuadratic Systems Objective Content Standards A.REI.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables... A.REI.11 Explain why the x-coordinates
More informationFoundations of Math II Unit 5: Solving Equations
Foundations of Math II Unit 5: Solving Equations Academics High School Mathematics 5.1 Warm Up Solving Linear Equations Using Graphing, Tables, and Algebraic Properties On the graph below, graph the following
More informationLecture 7: Sections 2.3 and 2.4 Rational and Exponential Functions. Recall that a power function has the form f(x) = x r where r is a real number.
L7-1 Lecture 7: Sections 2.3 and 2.4 Rational and Exponential Functions Recall that a power function has the form f(x) = x r where r is a real number. f(x) = x 1/2 f(x) = x 1/3 ex. Sketch the graph of
More informationMarch 5, 2009 Name The problems count as marked. The total number of points available is 131. Throughout this test, show your work.
March 5, 2009 Name The problems count as marked. The total number of points available is 131. Throughout this test, show your work. 1. (12 points) Consider the cubic curve f(x) = 2x 3 + 3x + 2. (a) What
More information3.4 The Fundamental Theorem of Algebra
333371_0304.qxp 12/27/06 1:28 PM Page 291 3.4 The Fundamental Theorem of Algebra Section 3.4 The Fundamental Theorem of Algebra 291 The Fundamental Theorem of Algebra You know that an nth-degree polynomial
More informationGeometry Summer Assignment 2018
Geometry Summer Assignment 2018 The following packet contains topics and definitions that you will be required to know in order to succeed in Geometry this year. You are advised to be familiar with each
More information4.1 Identifying Linear Functions
Warm-up Solve the equation for y. Then graph. 1. 2x - 3y = 12 4.1 Identifying Linear Functions I can... 1.) identify a linear function by a graph 2.) identify a linear function by ordered pairs (table)
More informationSummer Review. For Students Entering. Algebra 2 & Analysis
Lawrence High School Math Department Summer Review For Students Entering Algebra 2 & Analysis Fraction Rules: Operation Explanation Example Multiply Fractions Multiply both numerators and denominators
More informationMini Lecture 2.1 Introduction to Functions
Mini Lecture.1 Introduction to Functions 1. Find the domain and range of a relation.. Determine whether a relation is a function. 3. Evaluate a function. 1. Find the domain and range of the relation. a.
More information2/3. Activity 3: Adding and Subtracting Unlike Proper Fractions: (Answer all questions using correct spelling and grammar.)
Activity : Adding and Subtracting Unlike Proper Fractions: (Answer all questions using correct spelling and grammar.) The Unit Grid will be introduced for working with Unlike Proper Fractions. We will
More informationKey Features of a Graph. Warm Up What do you think the key features are of a graph? Write them down.
Warm Up What do you think the key features are of a graph? Write them down. 1 Domain and Range x intercepts and y intercepts Intervals of increasing, decreasing, and constant behavior Parent Equations
More informationChapter 8. Exploring Polynomial Functions. Jennifer Huss
Chapter 8 Exploring Polynomial Functions Jennifer Huss 8-1 Polynomial Functions The degree of a polynomial is determined by the greatest exponent when there is only one variable (x) in the polynomial Polynomial
More informationName: Date: Block: Algebra 1 Function/Solving for a Variable STUDY GUIDE
Algebra Functions Test STUDY GUIDE Name: Date: Block: SOLs: A.7, A. Algebra Function/Solving for a Variable STUDY GUIDE Know how to Plot points on a Cartesian coordinate plane. Find the (x, y) coordinates
More information1.2 Functions and Their Properties Name:
1.2 Functions and Their Properties Name: Objectives: Students will be able to represent functions numerically, algebraically, and graphically, determine the domain and range for functions, and analyze
More informationL Hopital s Rule. We will use our knowledge of derivatives in order to evaluate limits that produce indeterminate forms.
L Hopital s Rule We will use our knowledge of derivatives in order to evaluate its that produce indeterminate forms. Indeterminate Limits Main Idea x c f x g x If, when taking the it as x c, you get an
More informationQuadratic function and equations Quadratic function/equations, supply, demand, market equilibrium
Exercises 8 Quadratic function and equations Quadratic function/equations, supply, demand, market equilibrium Objectives - know and understand the relation between a quadratic function and a quadratic
More information5. Find the slope intercept equation of the line parallel to y = 3x + 1 through the point (4, 5).
Rewrite using rational eponents. 2 1. 2. 5 5. 8 4 4. 4 5. Find the slope intercept equation of the line parallel to y = + 1 through the point (4, 5). 6. Use the limit definition to find the derivative
More informationLesson: Slope. Warm Up. Unit #2: Linear Equations. 2) If f(x) = 7x 5, find the value of the following: f( 2) f(3) f(0)
Warm Up 1) 2) If f(x) = 7x 5, find the value of the following: f( 2) f(3) f(0) Oct 15 10:21 AM Unit #2: Linear Equations Lesson: Slope Oct 15 10:05 AM 1 Students will be able to find the slope Oct 16 12:19
More informationPreCalculus: Semester 1 Final Exam Review
Name: Class: Date: ID: A PreCalculus: Semester 1 Final Exam Review Short Answer 1. Determine whether the relation represents a function. If it is a function, state the domain and range. 9. Find the domain
More informationFinal Exam A Name. 20 i C) Solve the equation by factoring. 4) x2 = x + 30 A) {-5, 6} B) {5, 6} C) {1, 30} D) {-5, -6} -9 ± i 3 14
Final Exam A Name First, write the value(s) that make the denominator(s) zero. Then solve the equation. 1 1) x + 3 + 5 x - 3 = 30 (x + 3)(x - 3) 1) A) x -3, 3; B) x -3, 3; {4} C) No restrictions; {3} D)
More informationSection 4.1: Polynomial Functions and Models
Section 4.1: Polynomial Functions and Models Learning Objectives: 1. Identify Polynomial Functions and Their Degree 2. Graph Polynomial Functions Using Transformations 3. Identify the Real Zeros of a Polynomial
More information2.2 BEGINS: POLYNOMIAL
CHAPTER 2.2 HIGHER DEGREE POLY S 2.2 BEGINS: POLYNOMIAL Graphs of Polynomial Functions Polynomial functions are continuous. What this means to us is that the graphs of polynomial functions have no breaks,
More informationName Period. Date: have an. Essential Question: Does the function ( ) inverse function? Explain your answer.
Name Period Date: Topic: 10-3 Composition and Inverses of Functions Essential Question: Does the function inverse function? Explain your answer. have an Standard: F-BF.1c Objective: Compose functions.
More informationHomework 5 Solutions
Homework 5 Solutions ECS 0 (Fall 17) Patrice Koehl koehl@cs.ucdavis.edu ovember 1, 017 Exercise 1 a) Show that the following statement is true: If there exists a real number x such that x 4 +1 = 0, then
More informationMAT 122 Homework 7 Solutions
MAT 1 Homework 7 Solutions Section 3.3, Problem 4 For the function w = (t + 1) 100, we take the inside function to be z = t + 1 and the outside function to be z 100. The derivative of the inside function
More informationPre-Algebra 2. Unit 9. Polynomials Name Period
Pre-Algebra Unit 9 Polynomials Name Period 9.1A Add, Subtract, and Multiplying Polynomials (non-complex) Explain Add the following polynomials: 1) ( ) ( ) ) ( ) ( ) Subtract the following polynomials:
More informationMATH HISTORY ACTIVITY
A. Fisher Acf 92 workbook TABLE OF CONTENTS: Math History Activity. p. 2 3 Simplify Expressions with Integers p. 4 Simplify Expressions with Fractions.. p. 5 Simplify Expressions with Decimals.. p. 6 Laws
More informationThe Graphs of Polynomial Functions
Section 4.3 The Graphs of Polynomial Functions Objective 1: Understanding the Definition of a Polynomial Function Definition Polynomial Function n n 1 n 2 The function f() x = anx + an 1x + an 2x + L +
More informationUnit 3 Day 13 Review 1
Unit 3 Day 13 Review 1 Warm-up! Graph the following functions, with at least 4 points. Find the domain and range. Then, tell how they are changed from their parent graph. (Hint: Remember that the order
More informationDirect Variation. Graph the data is the chart on the next slide. Find the rate of change. April 30, Direct variation lesson.notebook.
Direct Variation Opener Marshall bought delicious beef biscuits at the bulk food store. The cost was $1.10 for 100 g. Here is a table of costs for different masses. Mass of beef biscuits (g) Costs ($)
More informationAP Calculus AB 2nd Semester Homework List
AP Calculus AB 2nd Semester Homework List Date Assigned: 1/4 DUE Date: 1/6 Title: Typsetting Basic L A TEX and Sigma Notation Write the homework out on paper. Then type the homework on L A TEX. Use this
More informationChapter 7: Exponents
Chapter : Exponents Algebra Chapter Notes Name: Algebra Homework: Chapter (Homework is listed by date assigned; homework is due the following class period) HW# Date In-Class Homework M / Review of Sections.-.
More informationInstructor Quick Check: Question Block 12
Instructor Quick Check: Question Block 2 How to Administer the Quick Check: The Quick Check consists of two parts: an Instructor portion which includes solutions and a Student portion with problems for
More informationSTEP 1: Ask Do I know the SLOPE of the line? (Notice how it s needed for both!) YES! NO! But, I have two NO! But, my line is
EQUATIONS OF LINES 1. Writing Equations of Lines There are many ways to define a line, but for today, let s think of a LINE as a collection of points such that the slope between any two of those points
More informationConcept: Solving Absolute Value Equations
Concept: Solving Absolute Value Equations Warm Up Name: 1. Determine what values of x make each inequality true. Graph each answer. (a) 9 x - 2 7 x + 8 9 x - 2 7 x + 8-7x) 2 x - 2 8 +2) 2 x 10 2) x 5 Remember:
More informationPolynomials Patterns Task
Polynomials Patterns Task Mathematical Goals Roughly sketch the graphs of simple polynomial functions by hand Graph polynomial functions using technology Identify key features of the graphs of polynomial
More informationIf you have completed your extra credit opportunity, please place it on your inbox.
Warm-Up If you have completed your extra credit opportunity, please place it on your inbox. On everyone s desk should be paper and a pencil for notes. We are covering all of Quarter 1 in one day, so we
More informationLesson 5b Solving Quadratic Equations
Lesson 5b Solving Quadratic Equations In this lesson, we will continue our work with Quadratics in this lesson and will learn several methods for solving quadratic equations. The first section will introduce
More informationAlgebra II Through Competitions Chapter 7 Function Composition and Operations
. FUNCTIONS. Definition A function is a relationship between the independent variable x and dependent variable y. Each value of x corresponds exactly one value of y. Note two different values of x can
More informationLIMITS AT INFINITY MR. VELAZQUEZ AP CALCULUS
LIMITS AT INFINITY MR. VELAZQUEZ AP CALCULUS RECALL: VERTICAL ASYMPTOTES Remember that for a rational function, vertical asymptotes occur at values of x = a which have infinite its (either positive or
More informationWhen a function is defined by a fraction, the denominator of that fraction cannot be equal to zero
As stated in the previous lesson, when changing from a function to its inverse the inputs and outputs of the original function are switched, because we take the original function and solve for x. This
More informationDefine the word inequality
Warm Up: Define the word inequality Agenda: Objective- Students can solve linear inequalities in one variable, including equations with coefficients represented by letters. Define Inequalities One & Two
More information( ) c. m = 0, 1 2, 3 4
G Linear Functions Probably the most important concept from precalculus that is required for differential calculus is that of linear functions The formulas you need to know backwards and forwards are:
More informationDay 4 ~ Increasing/Decreasing, and Extrema. A Graphical Approach
Day 4 ~ Increasing/Decreasing, and Extrema A Graphical Approach Warm Up ~ Day 4 1) Find the a) domain b) x & y intercepts c) range d) discontinuities e) end behavior using limit notation ) g( x) 3x 7x
More information