Graphing Linear Functions The collection of all input values is called the of a function.
|
|
- Antonia Pope
- 6 years ago
- Views:
Transcription
1 Math /7 NTES (9.3) Name Graphing Linear Functions The collection of all input values is called the of a function. The collection of all output values is called the of a function. Make a table for the function. Identif the range of the function. 1. f() = Domain: 0, 1,, 3. = + Domain: 11, 15,, 7 3. = 3 Domain: 5, 9, 1, 19 f() = f() = + f() = 3 Range: Range: Range:. You have a bo with 7 plants that ou are planting in a garden. Write a rule for as the function of, where is the number of plants ou have left in the bo; is the number of plants ou have put in the garden so far. a) In the beginning =, =. b) Each time ou put one plant in the garden, ou have one less plant in the bo, so = f() = c) Make a table and build the graph f() (, ) d) Domain Range e) What are the coordinates of the point of intersection of the graph and the -ais? What does -intercept represent? f) What does the point P represent? g) What are the coordinates of the point of intersection of the graph and the -ais? What does -intercept represent?
2 Find each function value. 5. f() if f() = +. f(9) if f() = 7. f(3) if f() = + Complete the function table. Then graph the function int: -int: -int: ; -int: ; Identif the -intercept and the -intercept of the graph int: ; -int: -int: ; -int: -int: ; -int: Graph each function
3 Math /7 Practice (9.3) Questions 1. Determine whether the relation is a function. Eplain {(5, 9), (, ), ( 7, ), (0, ), (, ), (3, 9), ( 3, )}. {(3, 9), (, ), ( 7, ), (0, ), (, ), (3, 5), ( 3, )} Questions 7-, Use the chart to answers. Determine whether the relation is a function. Eplain. 7. Describe how the area of a square is related to the length of the side. a. As the length of the side increases, the area decreases. b. As the length of the side increases, the area increases and then decreases. c. As the length of the side increases, the area increases. d. As the length of the side increases, the area decreases and then increases.. Is the relation (side length, area) a function? Eplain. a. No, there is a side length with areas paired with it. b. No, there are no negative area values. c. No, one side length is equal to the area value. d. Yes, each side length is paired with onl one value for the area. Area of a Square Side Length Area (cm ) (cm) Which set of ordered pairs are solutions to the following function? 9. = -3 a. b. c. d.
4 Math /7 Homework (9.3) Identif the -intercept and the -intercept of the graph int: ; -int: -int: ; -int: -int: ; -int:. The table shows the apparent temperature P F, as it feels to our bod, as a function of the real air temperature A F when there is 10% humidit. Graph the function. Air temperature ( F), A Apparent temperature ( F), P Rule of the function: P = Find each function value. 5. f() if f() = +. f(9) if f() = 7. f(3) if f() = + f() = f(9) = f(3) = Graph each function.. f() = 9. f() = f() = (,f()) 3 (,f()) f()
5 Math /7 Enrichment (9.3) A function flowchart and ten numbers are given below. Input each number into the flowchart at the place marked START, then follow the number through the flowchart. When ou reach the place marked STP, record the output number.
6 - NAME DATE PERID Stud Guide and Intervention Linear Equations in Two Variables A function can be represented with an equation. An equation such as 1.50 is called a linear equation. A linear equation in two variables is an equation in which the variables appear in separate terms and neither variable contains an eponent other than 1. Linear Equations 1,, 1 3 Nonlinear Equations 1, 3, 3, Solutions of a linear equation are ordered pairs that make the equation true. ne wa to find solutions is to make a table. Eample 1 Eample Complete the table. Use the results to write four solutions of 10. Write the solution as ordered pairs. 10 (, ) 1 ( 1) 10 1 ( 1, 1) 0 (0) (0, 10) 1 (1) 10 (1, ) () 10 (, ) A linear equation can also be represented b a graph. The coordinates of all points on a line are solutions to the equation. Graph 10 b plotting ordered pairs. Plot the points found in Eample 1. Connect the points using a straight line. (, ) (1, ) 10 (0, 10) 1 1 Eercises Find four solutions of each equation. Write the solutions as ordered pairs Sample answers are given ( 1, ), (0, ), ( 1, ), (0, 7), ( 1, 9), (0, 5), (1, ), (, ) (1, 10), (, 13) (1, 1), (, 3) Graph each equation b plotting ordered pairs Glencoe/McGraw-Hill Glencoe Pre-Algebra
7 - NAME DATE PERID Practice Linear Equations in Two Variables Find four solutions of each equation. Write the solutions as ordered pairs. 1. Sample answers are given ( 1, ), (0, 5), ( 1, 7), (0, 7), ( 1, ), (0, 1), (1, ), (, 3) (1, 7), (, 7) (1, ), (, 5) ( 1, 7), (0, ), ( 1, ), (0, ), ( 1, 1), (0, 1), (1, 5), (, ) (1, ), (, ) (1, 7), (, 0) Graph each equation b plotting ordered pairs CKING For Eercises 13 15, use the following information. Kirsten is making gingerbread cookies using her grandmother s recipe and needs to convert grams to ounces. The equation 0.0 describes the approimate number of ounces in grams. 13. Find three ordered pairs of values that satisf this equation. Sample answer: (100, ), (00, ), (300, 1) 1. Draw the graph that contains these points. 15. Do negative values of make sense in this case? Eplain. No; a recipe cannot contain a negative number of grams of an ingredient. Glencoe/McGraw-Hill Glencoe Pre-Algebra unces Grams
8 - NAME DATE PERID Enrichment Equations with Two Variables Complete the table for each equation Glencoe/McGraw-Hill Glencoe Pre-Algebra
9
10 -3 NAME DATE PERID Stud Guide and Intervention Graphing Linear Equations Using Intercepts Finding Intercepts The -intercept is the -coordinate of a point where a graph crosses the -ais. The -coordinate of this point is 0. The -intercept is the -coordinate of a point where a graph crosses the -ais. The -coordinate of this point is 0. To find the -intercept, let 0 in the equation and solve for. To find the -intercept, let 0 in the equation and solve for. Eample 1 Find the -intercept and the -intercept for the graph of To find the -intercept, let Write the equation. 5(0) 10 Replace with 0. 5 Simplif. To find the -intercept, let Write the equation. Eample (0, ) 5 10 (5, 0) Graph (0) 5 10 Replace with 0. Simplif. Eercises Find the -intercept and the -intercept for the graph of each equation ; 5 none; 1 ; Graph each equation using the - and -intercepts. Lesson ( 1, 0) (0, 3) (0, 9) 3 (9, 0) 9 1 ( 5, 0) (0, 5) Glencoe/McGraw-Hill 7 Glencoe Pre-Algebra
11 -3 NAME DATE PERID Skills Practice Graphing Linear Equations Using Intercepts State the -intercept and the -intercept of each line ; none; ; Find the -intercept and the -intercept for the graph of each equation ; 1 10; ; ; 1 1 ; none; 7 Graph each equation using the - and -intercepts (0, ) + (3, 0) (0, ) (0, ) + ( 1, 0) (0, 3) 3 (0, ) (5, 0) 5 (, 0) (3, 0) Glencoe/McGraw-Hill Glencoe Pre-Algebra
12 -3 NAME DATE PERID Practice Graphing Linear Equations Using Intercepts Find the -intercept and the -intercept for the graph of each equation , none, 3, , 3, 5 7, none Graph each equation using the - and -intercepts (7, 0) (0, 7) (0, 5) + 5 (5, 0) (0, ) (, 0) ( 7, 0) (0, 1) (0, 5) (, 0) (, 0) Lesson SAVINGS Rashid s grandparents started a savings account for him, contributing $1000. He deposits $30 each month into the account. The equation represents how much mone is in the savings account after number of months. Graph the equation and eplain what the -intercept means. The -intercept 1000 shows how much mone was in the savings account before Rashid made an deposits. $ (thousand) Months Glencoe/McGraw-Hill 9 Glencoe Pre-Algebra
NAME DATE PERIOD. Study Guide and Intervention. Ax + By = C, where A 0, A and B are not both zero, and A, B, and C are integers with GCF of 1.
NAME DATE PERID 3-1 Stud Guide and Intervention Identif Linear Equations and Intercepts A linear equation is an equation that can be written in the form A + B = C. This is called the standard form of a
More informationStudy Guide and Intervention
- Slope Stud Guide and Intervention Slope change in Slope m of a Line For points (, ) and (, ), where, m change in Eample Eample Determine the slope of the line that passes through (, ) and (, ). m Slope
More informationNAME DATE PERIOD. Study Guide and Intervention. Transformations of Quadratic Graphs
NAME DATE PERID Stud Guide and Intervention Write Quadratic Equations in Verte Form A quadratic function is easier to graph when it is in verte form. You can write a quadratic function of the form = a
More informationNAME DATE PERIOD. Study Guide and Intervention. Ax + By = C, where A 0, A and B are not both zero, and A, B, and C are integers with GCF of 1.
NAME DATE PERID 3-1 Stud Guide and Intervention Graphing Linear Equations Identif Linear Equations and Intercepts A linear equation is an equation that can be written in the form A + B = C. This is called
More informationNAME DATE PERIOD. Study Guide and Intervention
NAME DATE PERID Stud Guide and Intervention Graph To graph a quadratic inequalit in two variables, use the following steps: 1. Graph the related quadratic equation, = a 2 + b + c. Use a dashed line for
More informationSystems of Linear Equations: Solving by Graphing
8.1 Sstems of Linear Equations: Solving b Graphing 8.1 OBJECTIVE 1. Find the solution(s) for a set of linear equations b graphing NOTE There is no other ordered pair that satisfies both equations. From
More informationChapter 8 Resource Masters
Chapter Resource Masters Consumable Workbooks Man of the worksheets contained in the Chapter Resource Masters booklets are available as consumable workbooks in both English and Spanish. Stud Guide and
More informationf(x) = 2x 2 + 2x - 4
4-1 Graphing Quadratic Functions What You ll Learn Scan the tet under the Now heading. List two things ou will learn about in the lesson. 1. Active Vocabular 2. New Vocabular Label each bo with the terms
More information6-1 Study Guide and Intervention
NAME DATE PERID 6- Stud Guide and Intervention Graphing Sstems of Equations Possible Number of Solutions Two or more linear equations involving the same variables form a sstem of equations. A solution
More informationHow can you write an equation of a line when you are given the slope and a point on the line? ACTIVITY: Writing Equations of Lines
.7 Writing Equations in Point-Slope Form How can ou write an equation of a line when ou are given the slope and a point on the line? ACTIVITY: Writing Equations of Lines Work with a partner. Sketch the
More informationStudy Guide and Intervention
6- NAME DATE PERID Stud Guide and Intervention Graphing Quadratic Functions Graph Quadratic Functions Quadratic Function A function defined b an equation of the form f () a b c, where a 0 b Graph of a
More informationHow can you determine the number of solutions of a quadratic equation of the form ax 2 + c = 0? ACTIVITY: The Number of Solutions of ax 2 + c = 0
9. Solving Quadratic Equations Using Square Roots How can ou determine the number of solutions of a quadratic equation of the form a + c = 0? ACTIVITY: The Number of Solutions of a + c = 0 Work with a
More information9-1. The Function with Equation y = ax 2. Vocabulary. Graphing y = x 2. Lesson
Chapter 9 Lesson 9-1 The Function with Equation = a BIG IDEA The graph of an quadratic function with equation = a, with a 0, is a parabola with verte at the origin. Vocabular parabola refl ection-smmetric
More information7-3 Skills Practice. Square Root Functions and Inequalities. Lesson 7-3. Graph each function. State the domain and range of each function.
NAME DATE PERID 7- Skills Practice Square Root Functions and Inequalities Graph each function. State the domain and range of each function...... 6. Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill
More informationWriting Equations in Point-Slope Form
. Writing Equations in Point-Slope Form Essential Question How can ou write an equation of a line when ou are given the slope and a point on the line? Writing Equations of Lines Work with a partner. Sketch
More informationReady To Go On? Skills Intervention 2-1 Solving Linear Equations and Inequalities
A Read To Go n? Skills Intervention -1 Solving Linear Equations and Inequalities Find these vocabular words in Lesson -1 and the Multilingual Glossar. Vocabular equation solution of an equation linear
More informationLesson 4.1 Exercises, pages
Lesson 4.1 Eercises, pages 57 61 When approimating answers, round to the nearest tenth. A 4. Identify the y-intercept of the graph of each quadratic function. a) y = - 1 + 5-1 b) y = 3-14 + 5 Use mental
More informationNAME DATE PERIOD. Study Guide and Intervention. Solving Rational Equations and Inequalities
NAME DATE PERIOD Solve Rational Equations A rational equation contains one or more rational epressions. To solve a rational equation, first multipl each side b the least common denominator of all of the
More information4.6 Model Direct Variation
4.6 Model Direct Variation Goal p Write and graph direct variation equations. Your Notes VOCABULARY Direct variation Constant of variation Eample Identif direct variation equations Tell whether the equation
More informationLesson 8.2 Exercises, pages
Lesson 8. Eercises, pages 38 A Students should verif the solutions to all equations.. Which values of are not roots of each equation? a) ƒ - 3 ƒ = 7 = 5 or =- Use mental math. 5: L.S. 7 R.S. 7 : L.S. 7
More informationComparing Linear and Nonlinear Functions 5.5. ACTIVITY: Finding Patterns for Similar Figures. How can you recognize when a pattern
5.5 Comparing Linear and Nonlinear Functions in real life is linear or nonlinear? How can ou recognize when a pattern ACTIVITY: Finding Patterns for Similar Figures Work with a partner. Cop and complete
More informationRELATIONS AND FUNCTIONS through
RELATIONS AND FUNCTIONS 11.1.2 through 11.1. Relations and Functions establish a correspondence between the input values (usuall ) and the output values (usuall ) according to the particular relation or
More informationSolving Polynomial Equations Exponential Growth in Factored Form
7.5 Solving Polnomial Equations Eponential Growth in Factored Form is written in factored form? How can ou solve a polnomial equation that Two polnomial equations are equivalent when the have the same
More information2.1 Evaluate and Graph Polynomial
2. Evaluate and Graph Polnomial Functions Georgia Performance Standard(s) MM3Ab, MM3Ac, MM3Ad Your Notes Goal p Evaluate and graph polnomial functions. VOCABULARY Polnomial Polnomial function Degree of
More information) approaches e
COMMON CORE Learning Standards HSF-IF.C.7e HSF-LE.B.5. USING TOOLS STRATEGICALLY To be proficient in math, ou need to use technological tools to eplore and deepen our understanding of concepts. The Natural
More informationStudy Guide and Intervention
Study Guide and Intervention Extending the pattern below shows that = or. 2 0 This suggests the following definition. a n = a n, for a 0 and any integer n. Example a. 3 b. y 2 3 3 y 2 y 2 We can evaluate
More informationLesson 3.1 Linear Equations and Arithmetic Sequences
Lesson 3.1 Linear Equations and Arithmetic Sequences 1. Find an eplicit formula for each recursivel defined arithmetic sequence. a. u 0 18.25 b. t 0 0 u n u n 1 4.75 where n 1 t n t n 1 100 where n 1 2.
More informationNAME DATE PERIOD. Study Guide and Intervention. Solving Quadratic Equations by Graphing. 2a = -
NAME DATE PERID - Study Guide and Intervention Solving Quadratic Equations by Graphing Solve Quadratic Equations Quadratic Equation A quadratic equation has the form a + b + c = 0, where a 0. Roots of
More informationStudy Guide and Intervention. The Quadratic Formula and the Discriminant. Quadratic Formula. Replace a with 1, b with -5, and c with -14.
Study Guide and Intervention Quadratic Formula The Quadratic Formula can be used to solve any quadratic equation once it is written in the form a 2 + b + c = 0. Quadratic Formula The solutions of a 2 +
More informationStudy Guide and Intervention
7-3 Study Guide and Intervention Elimination Using Addition and Subtraction Elimination Using Addition In systems of equations in which the coefficients of the x or y terms are additive inverses, solve
More information7.5 Solve Special Types of
75 Solve Special Tpes of Linear Sstems Goal p Identif the number of of a linear sstem Your Notes VOCABULARY Inconsistent sstem Consistent dependent sstem Eample A linear sstem with no Show that the linear
More informationUsing Intercept Form
8.5 Using Intercept Form Essential Question What are some of the characteristics of the graph of f () = a( p)( q)? Using Zeros to Write Functions Work with a partner. Each graph represents a function of
More informationComparing Linear, Exponential, and Quadratic Functions
. Comparing Linear, Eponential, and Quadratic Functions How can ou compare the growth rates of linear, eponential, and quadratic functions? ACTIVITY: Comparing Speeds Work with a partner. Three cars start
More informationLesson Remember. Finding Domain and Range from a Graph EXAMPLE. Key Vocabulary
0. Lesson Ke Vocabular function domain range function form Functions A function is a relationship that pairs each input with eactl one output. The domain is the set of all possible input values. The range
More informationStart at the origin. Move left 3 units since the x-coordinate. Start at the origin. Since the x-coordinate is 0, the point
Answers (Lesson -) Lesson - - Stud Guide and Intervention The Coordinate Plane Identif Points In the diagram at the right, points are located in reference to two perpendicular number lines called aes.
More informationEssential Question How can you solve a nonlinear system of equations?
.5 Solving Nonlinear Sstems Essential Question Essential Question How can ou solve a nonlinear sstem of equations? Solving Nonlinear Sstems of Equations Work with a partner. Match each sstem with its graph.
More information15.2 Graphing Logarithmic
_ - - - - - - Locker LESSON 5. Graphing Logarithmic Functions Teas Math Standards The student is epected to: A.5.A Determine the effects on the ke attributes on the graphs of f () = b and f () = log b
More information15.4 Equation of a Circle
Name Class Date 1.4 Equation of a Circle Essential Question: How can ou write the equation of a circle if ou know its radius and the coordinates of its center? Eplore G.1.E Show the equation of a circle
More informationLESSON #24 - POWER FUNCTIONS COMMON CORE ALGEBRA II
1 LESSON #4 - POWER FUNCTIONS COMMON CORE ALGEBRA II Before we start to analze polnomials of degree higher than two (quadratics), we first will look at ver simple functions known as power functions. The
More informationReady To Go On? Skills Intervention 5-1 Using Transformations to Graph Quadratic Functions
Read To Go On? Skills Intervention 5-1 Using Transformations to Graph Quadratic Functions Find these vocabular words in Lesson 5-1 and the Multilingual Glossar. Vocabular quadratic function parabola verte
More information(2.5) 1. Solve the following compound inequality and graph the solution set.
Intermediate Algebra Practice Final Math 0 (7 th ed.) (Ch. -) (.5). Solve the following compound inequalit and graph the solution set. 0 and and > or or (.7). Solve the following absolute value inequalities.
More informationSkills Practice 8-9. Solving Systems of Equations. (1, 2) no solution (0, 2) (1, 3) infinitely many ( 2, 0) (4, 3) (2, 2) (12, 4) (3, 2) (13, 3)
8-9 NME TE PERI Skills Practice Solving Sstems of Equations Solve each sstem of equations b graphing. 1. 4.. 4 8 (1, ) 4 8 (0, ) (1, ) no solution (0, ) 4. 4 5. 4 1 6. 4 1 4 4 1 (1, ) 4 4 (, 0) 4 (1, )
More information6.4 graphs OF logarithmic FUnCTIOnS
SECTION 6. graphs of logarithmic functions 9 9 learning ObjeCTIveS In this section, ou will: Identif the domain of a logarithmic function. Graph logarithmic functions. 6. graphs OF logarithmic FUnCTIOnS
More information3.2 LOGARITHMIC FUNCTIONS AND THEIR GRAPHS
Section. Logarithmic Functions and Their Graphs 7. LOGARITHMIC FUNCTIONS AND THEIR GRAPHS Ariel Skelle/Corbis What ou should learn Recognize and evaluate logarithmic functions with base a. Graph logarithmic
More informationFunctions. Essential Question What are some of the characteristics of the graph of an exponential function? ) x e. f (x) = ( 1 3 ) x f.
7. TEXAS ESSENTIAL KNOWLEDGE AND SKILLS A..A Eponential Growth and Deca Functions Essential Question What are some of the characteristics of the graph of an eponential function? You can use a graphing
More informationCan a system of linear equations have no solution? Can a system of linear equations have many solutions?
5. Solving Special Sstems of Linear Equations Can a sstem of linear equations have no solution? Can a sstem of linear equations have man solutions? ACTIVITY: Writing a Sstem of Linear Equations Work with
More informationPACKET Unit 4 Honors ICM Functions and Limits 1
PACKET Unit 4 Honors ICM Functions and Limits 1 Day 1 Homework For each of the rational functions find: a. domain b. -intercept(s) c. y-intercept Graph #8 and #10 with at least 5 EXACT points. 1. f 6.
More informationLESSON #42 - INVERSES OF FUNCTIONS AND FUNCTION NOTATION PART 2 COMMON CORE ALGEBRA II
LESSON #4 - INVERSES OF FUNCTIONS AND FUNCTION NOTATION PART COMMON CORE ALGEBRA II You will recall from unit 1 that in order to find the inverse of a function, ou must switch and and solve for. Also,
More informationLesson 3.1 Linear Equations and Arithmetic Sequences
Lesson 3.1 Linear Equations and Arithmetic Sequences 1. Find an eplicit formula for each recursivel defined arithmetic sequence. a. u 0 18.25 b. t 0 0 u n u n 1 4.75 where n 1 t n t n 1 100 where n 1 2.
More informationSample. Sample. Sample. Sample (1,2) (-1,1) (3,-1) (-3,-5) Sample (1,2) (-1,1) (3,-1) (-3,-5) Sample. (x, y) Domain: {-3, -1, 1, 3} (1,2) (-1,1)
(-1,1) (1,2) Algebra 2 HS Mathematics Unit: 02 Lesson: 01 (3,-1) (-3,-5) Range: {-5, 1, 2, -1} (-1,1) (-3,-5) (1,2) (3,-1) (-1,1) (-3,-5) (1,2) (3,-1) Domain: {-3, -1, 1, 3} (1,2) (-1,1) (3,-1) (-3,-5)
More informationSolving Quadratic Equations by Graphing 9.1. ACTIVITY: Solving a Quadratic Equation by Graphing. How can you use a graph to solve a quadratic
9. Solving Quadratic Equations b Graphing equation in one variable? How can ou use a graph to solve a quadratic Earlier in the book, ou learned that the -intercept of the graph of = a + b variables is
More informationChapter 2 Resource Masters
Chapter Resource Masters Consumable Workbooks Man of the worksheets contained in the Chapter Resource Masters booklets are available as consumable workbooks. Stud Guide and Intervention Workbook 0-07-8809-X
More informationMath 115: Review for Chapter 2
Math 5: Review for Chapter Can ou determine algebraicall whether an equation is smmetric with respect to the - ais, the -ais, or the origin?. Algebraicall determine whether each equation below is smmetric
More informationReady To Go On? Skills Intervention 6-1 Polynomials
6A Read To Go On? Skills Intervention 6- Polnomials Find these vocabular words in Lesson 6- and the Multilingual Glossar. Vocabular monomial polnomial degree of a monomial degree of a polnomial leading
More informationSection 5.1: Functions
Objective: Identif functions and use correct notation to evaluate functions at numerical and variable values. A relationship is a matching of elements between two sets with the first set called the domain
More informationSOLVING SYSTEMS OF EQUATIONS
SOLVING SYSTEMS OF EQUATIONS 4.. 4..4 Students have been solving equations even before Algebra. Now the focus on what a solution means, both algebraicall and graphicall. B understanding the nature of solutions,
More informationGrowing, Growing, Growing Answers
Investigation Additional Practice. a. b. c. d.,,7 e. n.?.?.?,.?,. a. Color Branches 9 7 79 b. b c c. Color 7 would be used to draw,7 branches. d. Branching Pattern Branches Color Skill: Using Eponents...7......;...7.7;
More informationChapter 5 Resource Masters
Chapter Resource Masters Answers (Lesson -) Lesson - - Find Slope NAME DATE PERID Stud Guide and Intervention Slope Slope of a Line rise run m or m, where (, ) and (, ) are the coordinates of an two points
More informationLESSON #28 - POWER FUNCTIONS COMMON CORE ALGEBRA II
1 LESSON #8 - POWER FUNCTIONS COMMON CORE ALGEBRA II Before we start to analze polnomials of degree higher than two (quadratics), we first will look at ver simple functions known as power functions. The
More informationc) domain {x R, x 3}, range {y R}
Answers Chapter 1 Functions 1.1 Functions, Domain, and Range 1. a) Yes, no vertical line will pass through more than one point. b) No, an vertical line between = 6 and = 6 will pass through two points..
More informationMATH 021 UNIT 1 HOMEWORK ASSIGNMENTS
MATH 01 UNIT 1 HOMEWORK ASSIGNMENTS General Instructions You will notice that most of the homework assignments for a section have more than one part. Usuall, the part (A) questions ask for eplanations,
More informationSystems of Linear and Quadratic Equations. Check Skills You ll Need. y x. Solve by Graphing. Solve the following system by graphing.
NY- Learning Standards for Mathematics A.A. Solve a sstem of one linear and one quadratic equation in two variables, where onl factoring is required. A.G.9 Solve sstems of linear and quadratic equations
More informationThe Coordinate Plane and Linear Equations Algebra 1
Name: The Coordinate Plane and Linear Equations Algebra Date: We use the Cartesian Coordinate plane to locate points in two-dimensional space. We can do this b measuring the directed distances the point
More informationReady To Go On? Skills Intervention 7-1 Exponential Functions, Growth, and Decay
7A Find these vocabular words in Lesson 7-1 and the Multilingual Glossar. Vocabular Read To Go On? Skills Intervention 7-1 Eponential Functions, Growth, and Deca eponential growth eponential deca asmptote
More information15.2 Graphing Logarithmic
Name Class Date 15. Graphing Logarithmic Functions Essential Question: How is the graph of g () = a log b ( h) + k where b > and b 1 related to the graph of f () = log b? Resource Locker Eplore 1 Graphing
More informationLecture Guide. Math 90 - Intermediate Algebra. Stephen Toner. Intermediate Algebra, 2nd edition. Miller, O'Neill, & Hyde. Victor Valley College
Lecture Guide Math 90 - Intermediate Algebra to accompan Intermediate Algebra, 2nd edition Miller, O'Neill, & Hde Prepared b Stephen Toner Victor Valle College Last updated: 11/24/10 0 1.1 Sets of Numbers
More informationAlgebra Concepts Equation Solving Flow Chart Page 1 of 6. How Do I Solve This Equation?
Algebra Concepts Equation Solving Flow Chart Page of 6 How Do I Solve This Equation? First, simplify both sides of the equation as much as possible by: combining like terms, removing parentheses using
More informationFunctions. Essential Question What is a function?
3. Functions COMMON CORE Learning Standard HSF-IF.A. Essential Question What is a function? A relation pairs inputs with outputs. When a relation is given as ordered pairs, the -coordinates are inputs
More informationModel Inverse Variation. p Write and graph inverse variation equations. VOCABULARY. Inverse variation. Constant of variation. Branches of a hyperbola
12.1 Model Inverse Variation Goal p Write and graph inverse variation equations. Your Notes VOCABULARY Inverse variation Constant of variation Hperbola Branches of a hperbola Asmptotes of a hperbola Eample
More informationFunctions. Essential Question What is a function? Work with a partner. Functions can be described in many ways.
. Functions Essential Question What is a function? A relation pairs inputs with outputs. When a relation is given as ordered pairs, the -coordinates are inputs and the -coordinates are outputs. A relation
More informationdecreases as x increases.
Chapter Review FREQUENTLY ASKED Questions Q: How can ou identif an eponential function from its equation? its graph? a table of values? A: The eponential function has the form f () 5 b, where the variable
More information( 3x. Chapter Review. Review Key Vocabulary. Review Examples and Exercises 6.1 Properties of Square Roots (pp )
6 Chapter Review Review Ke Vocabular closed, p. 266 nth root, p. 278 eponential function, p. 286 eponential growth, p. 296 eponential growth function, p. 296 compound interest, p. 297 Vocabular Help eponential
More information3.2 Understanding Relations and Functions-NOTES
Name Class Date. Understanding Relations and Functions-NOTES Essential Question: How do ou represent relations and functions? Eplore A1.1.A decide whether relations represented verball, tabularl, graphicall,
More informationExponential and Logarithmic Functions
Eponential and Logarithmic Functions 6 Figure Electron micrograph of E. Coli bacteria (credit: Mattosaurus, Wikimedia Commons) CHAPTER OUTLINE 6. Eponential Functions 6. Logarithmic Properties 6. Graphs
More information2-1. Practice. Relations and Functions
NAME DATE PERID -1 Practice Relations and Functions State the domain and range of each relation. Then determine whether each relation is a function. If it is a function, determine if it is one-to-one,
More information( 7, 3) means x = 7 and y = 3. ( 7, 3) works in both equations so. Section 5 1: Solving a System of Linear Equations by Graphing
Section 5 : Solving a Sstem of Linear Equations b Graphing What is a sstem of Linear Equations? A sstem of linear equations is a list of two or more linear equations that each represents the graph of a
More informationVocabulary. Term Page Definition Clarifying Example degree of a monomial. degree of a polynomial. end behavior. leading coefficient.
CHAPTER 6 Vocabular The table contains important vocabular terms from Chapter 6. As ou work through the chapter, fill in the page number, definition, and a clarifing eample. Term Page Definition Clarifing
More information7-1. Exploring Exponential Models. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary. 1. Cross out the expressions that are NOT powers.
7-1 Eploring Eponential Models Vocabular Review 1. Cross out the epressions that are NOT powers. 16 6a 1 7. Circle the eponents in the epressions below. 5 6 5a z Vocabular Builder eponential deca (noun)
More information4.2 Start Thinking. 4.2 Warm Up. 4.2 Cumulative Review Warm Up
. Start Thinking How can ou find a linear equation from a graph for which ou do not know the -intercept? Describe a situation in which ou might know the slope but not the -intercept. Provide a graph of
More information15.2 Graphing Logarithmic
Name Class Date 15. Graphing Logarithmic Functions Essential Question: How is the graph of g () = a log b ( h) + k where b > 0 and b 1 related to the graph of f () = log b? Resource Locker A.5.A Determine
More informationA11.1 Areas under curves
Applications 11.1 Areas under curves A11.1 Areas under curves Before ou start You should be able to: calculate the value of given the value of in algebraic equations of curves calculate the area of a trapezium.
More information11.1 Solving Linear Systems by Graphing
Name Class Date 11.1 Solving Linear Sstems b Graphing Essential Question: How can ou find the solution of a sstem of linear equations b graphing? Resource Locker Eplore Tpes of Sstems of Linear Equations
More information4-1 Study Guide and Intervention
NAME DATE PERID 4-1 Study Guide and Intervention Graph Quadratic Functions Quadratic Function A function defined by an equation of the form = a 2 + b + c, where a 0 Graph of a Quadratic Function A parabola
More informationAlgebra 1 Skills Needed to be Successful in Algebra 2
Algebra 1 Skills Needed to be Successful in Algebra A. Simplifing Polnomial Epressions Objectives: The student will be able to: Appl the appropriate arithmetic operations and algebraic properties needed
More informationEssential Question: How can you solve equations involving variable exponents? Explore 1 Solving Exponential Equations Graphically
6 7 6 y 7 8 0 y 7 8 0 Locker LESSON 1 1 Using Graphs and Properties to Solve Equations with Eponents Common Core Math Standards The student is epected to: A-CED1 Create equations and inequalities in one
More information1.5. Analyzing Graphs of Functions. The Graph of a Function. What you should learn. Why you should learn it. 54 Chapter 1 Functions and Their Graphs
0_005.qd /7/05 8: AM Page 5 5 Chapter Functions and Their Graphs.5 Analzing Graphs of Functions What ou should learn Use the Vertical Line Test for functions. Find the zeros of functions. Determine intervals
More informationEssential Question What is the equation of a circle with center (h, k) and radius r in the coordinate plane?
10.7 Circles in the Coordinate Plane Essential Question What is the equation of a circle with center (h, k) and radius r in the coordinate plane? The Equation of a Circle with Center at the Origin Work
More informationMATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED
FOM 11 T7 GRAPHING LINEAR EQUATIONS REVIEW - 1 1 MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED 1) TWO VARIABLE EQUATIONS = an equation containing two different variables. ) COEFFICIENT = the number in front
More informationSolve Quadratic Equations by Graphing
0.3 Solve Quadratic Equations b Graphing Before You solved quadratic equations b factoring. Now You will solve quadratic equations b graphing. Wh? So ou can solve a problem about sports, as in Eample 6.
More informationMath 3201 UNIT 5: Polynomial Functions NOTES. Characteristics of Graphs and Equations of Polynomials Functions
1 Math 301 UNIT 5: Polnomial Functions NOTES Section 5.1 and 5.: Characteristics of Graphs and Equations of Polnomials Functions What is a polnomial function? Polnomial Function: - A function that contains
More information2 variables. is the same value as the solution of. 1 variable. You can use similar reasoning to solve quadratic equations. Work with a partner.
9. b Graphing Essential Question How can ou use a graph to solve a quadratic equation in one variable? Based on what ou learned about the -intercepts of a graph in Section., it follows that the -intercept
More informationACTIVITY: Comparing Types of Decay
6.6 Eponential Deca eponential deca? What are the characteristics of 1 ACTIVITY: Comparing Tpes of Deca Work with a partner. Describe the pattern of deca for each sequence and graph. Which of the patterns
More informationLaurie s Notes. Overview of Section 3.5
Overview of Section.5 Introduction Sstems of linear equations were solved in Algebra using substitution, elimination, and graphing. These same techniques are applied to nonlinear sstems in this lesson.
More information2 nd Semester Final Exam Review Block Date
Algebra 1B Name nd Semester Final Eam Review Block Date Calculator NOT Allowed Graph each function. Identif the verte and ais of smmetr. 1 (10-1) 1. (10-1). 3 (10-) 3. 4 7 (10-) 4. 3 6 4 (10-1) 5. Predict
More informationPractice A ( 1, 3 ( 0, 1. Match the function with its graph. 3 x. Explain how the graph of g can be obtained from the graph of f. 5 x.
8. Practice A For use with pages 65 7 Match the function with its graph.. f. f.. f 5. f 6. f f Lesson 8. A. B. C. (, 6) (0, ) (, ) (0, ) ( 0, ) (, ) D. E. F. (0, ) (, 6) ( 0, ) (, ) (, ) (0, ) Eplain how
More informationWhich of the following expressions are monomials?
9 1 Stud Guide Pages 382 387 Polnomials The epressions, 6, 5a 2, and 10cd 3 are eamples of monomials. A monomial is a number, a variable, or a product of numbers and variables. An eponents in a monomial
More informationLESSON 12.2 LOGS AND THEIR PROPERTIES
LESSON. LOGS AND THEIR PROPERTIES LESSON. LOGS AND THEIR PROPERTIES 5 OVERVIEW Here's what ou'll learn in this lesson: The Logarithm Function a. Converting from eponents to logarithms and from logarithms
More informationThe graphs intersect. Therefore, there is one solution. The. The solution is (3, 1). many solutions.
Answers (Lesson 7-) Lesson 7-7- NAME DATE PERID Stud Guide and Intervention Graphing Sstems of Equations Number of Solutions Two or more linear equations involving the same variables form a sstem of equations.
More informationChapter 6 Resource Masters
Chapter 6 Resource Masters Consumable Workbooks Man of the worksheets contained in the Chapter Resource Masters booklets are available as consumable workbooks. Stud Guide and Intervention Workbook 0-07-8809-X
More informationSYSTEMS OF THREE EQUATIONS
SYSTEMS OF THREE EQUATIONS 11.2.1 11.2.4 This section begins with students using technology to eplore graphing in three dimensions. By using strategies that they used for graphing in two dimensions, students
More information