Graphing Linear Equations: Warm Up: Brainstorm what you know about Graphing Lines: (Try to fill the whole page) Graphing

Similar documents
Math M111: Lecture Notes For Chapter 3

SB 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.

Functions & Graphs. Section 1.2

Homework 6. (x 3) 2 + (y 1) 2 = 25. (x 5) 2 + (y + 2) 2 = 49

Solve the problem. Determine the center and radius of the circle. Use the given information about a circle to find its equation.

Linear Equations. Find the domain and the range of the following set. {(4,5), (7,8), (-1,3), (3,3), (2,-3)}

Georgia Department of Education Common Core Georgia Performance Standards Framework CCGPS Advanced Algebra Unit 2

Unit 4 Day 4 & 5. Piecewise Functions

GUIDED NOTES 5.6 RATIONAL FUNCTIONS

Geometry/Trig Name: Date: Lesson 1-11 Writing the Equation of a Perpendicular Bisector


Solving Equations Quick Reference

( ) is called the dependent variable because its

Function Junction: Homework Examples from ACE

Chapter 2 notes from powerpoints

6-6 Solving Systems of Linear Inequalities 6-6. Solving Systems of Linear Inequalities

6-4 Solving Special Systems

b) since the remainder is 0 I need to factor the numerator. Synthetic division tells me this is true

Chapter 3: Inequalities, Lines and Circles, Introduction to Functions

Algebra I - Study Guide for Final

2. If the discriminant of a quadratic equation is zero, then there (A) are 2 imaginary roots (B) is 1 rational root

Algebra 2 and Trigonometry

L Hopital s Rule. We will use our knowledge of derivatives in order to evaluate limits that produce indeterminate forms.

ICM ~ Unit 4 ~ Day 3. Horizontal Asymptotes, End Behavior

Calculus I Sample Exam #01

CHAPTER 1: Functions

Math 3C Midterm 1 Study Guide

Example: f(x) = 2x² + 1 Solution: Math 2 VM Part 5 Quadratic Functions April 25, 2017

CHAPTER 2: Polynomial and Rational Functions

SOLUTIONS FOR PROBLEMS 1-30

2-7 Solving Quadratic Inequalities. ax 2 + bx + c > 0 (a 0)

Herndon High School Geometry Honors Summer Assignment

Unit 1: Polynomial Functions SuggestedTime:14 hours

Honors Advanced Algebra Unit 3: Polynomial Functions November 9, 2016 Task 11: Characteristics of Polynomial Functions

1 Lecture 25: Extreme values

MAC College Algebra

S4 (4.3) Quadratic Functions.notebook February 06, 2018

Pre Calculus with Mrs. Bluell

Review 1. 1 Relations and Functions. Review Problems

Algebra II (Common Core) Summer Assignment Due: September 11, 2017 (First full day of classes) Ms. Vella

Algebra 2 Summer Work Packet Review and Study Guide

Determine 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?

Unit 9: Quadratics Intercept Form

Homework 1. 3x 12, 61.P (x) = 3t 21 Section 1.2

Polynomial Review Problems

1,3. 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

(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)

V. Graph Sketching and Max-Min Problems

3 Polynomial and Rational Functions

8-1 Factors and Greatest Common Factors 8-1. Factors and Greatest Common Factors

A Library of Functions

Math 155 Prerequisite Review Handout

Quarter 2 400, , , , , , ,000 50,000

GUIDED NOTES 2.2 LINEAR EQUATIONS IN ONE VARIABLE

MHF4U. Advanced Functions Grade 12 University Mitchell District High School. Unit 3 Rational Functions & Equations 6 Video Lessons

Subtract 6 to both sides Divide by 2 on both sides. Cross Multiply. Answer: x = -9

Solving a Linear-Quadratic System

Foundations of Math II Unit 5: Solving Equations

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.

March 5, 2009 Name The problems count as marked. The total number of points available is 131. Throughout this test, show your work.

3.4 The Fundamental Theorem of Algebra

Geometry Summer Assignment 2018

4.1 Identifying Linear Functions

Summer Review. For Students Entering. Algebra 2 & Analysis

Mini Lecture 2.1 Introduction to Functions

2/3. Activity 3: Adding and Subtracting Unlike Proper Fractions: (Answer all questions using correct spelling and grammar.)

Key Features of a Graph. Warm Up What do you think the key features are of a graph? Write them down.

Chapter 8. Exploring Polynomial Functions. Jennifer Huss

Name: Date: Block: Algebra 1 Function/Solving for a Variable STUDY GUIDE

1.2 Functions and Their Properties Name:

L Hopital s Rule. We will use our knowledge of derivatives in order to evaluate limits that produce indeterminate forms.

Quadratic function and equations Quadratic function/equations, supply, demand, market equilibrium

5. Find the slope intercept equation of the line parallel to y = 3x + 1 through the point (4, 5).

Lesson: 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)

PreCalculus: Semester 1 Final Exam Review

Final 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

Section 4.1: Polynomial Functions and Models

2.2 BEGINS: POLYNOMIAL

Name Period. Date: have an. Essential Question: Does the function ( ) inverse function? Explain your answer.

Homework 5 Solutions

MAT 122 Homework 7 Solutions

Pre-Algebra 2. Unit 9. Polynomials Name Period

MATH HISTORY ACTIVITY

The Graphs of Polynomial Functions

Unit 3 Day 13 Review 1

Direct Variation. Graph the data is the chart on the next slide. Find the rate of change. April 30, Direct variation lesson.notebook.

AP Calculus AB 2nd Semester Homework List

Chapter 7: Exponents

Instructor Quick Check: Question Block 12

STEP 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

Concept: Solving Absolute Value Equations

Polynomials Patterns Task

If you have completed your extra credit opportunity, please place it on your inbox.

Lesson 5b Solving Quadratic Equations

Algebra II Through Competitions Chapter 7 Function Composition and Operations

LIMITS AT INFINITY MR. VELAZQUEZ AP CALCULUS

When a function is defined by a fraction, the denominator of that fraction cannot be equal to zero

Define the word inequality

( ) c. m = 0, 1 2, 3 4

Day 4 ~ Increasing/Decreasing, and Extrema. A Graphical Approach

Transcription:

Graphing Linear Equations: Warm Up: Brainstorm what you know about Graphing Lines: (Try to fill the whole page) Graphing

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

x 3 y 1 x = -3 Y = 4 y = x y x 3 Points to Remember: Homework:

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:

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:

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 121 1-29 eoo.

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 = 2 2. 6x + 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

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?

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

5. f (3) = 4, f(6) = -3 6. f(-1) = 2, f(2) = 2 Points to Remember: Homework: page 149 written exercises 1-21 odd

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)

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:

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 144 1-5 odd by hand show all work. 7-11 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.

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.

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:

2024 © sciencedocbox.com Privacy Policy | Terms of Service | Feedback