Functions. Essential Question What is a function? Work with a partner. Functions can be described in many ways.
|
|
- Debra Pope
- 6 years ago
- Views:
Transcription
1 . 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 that pairs each input with eactl one output is a function. Describing a Function Work with a partner. Functions can be described in man was. ANALYZING RELATIONSHIPS To be proficient in math, ou need to analze relationships mathematicall to draw conclusions. b an equation b an input-output table using words b a graph as a set of ordered pairs a. Eplain wh the graph shown represents a function. b. Describe the function in two other was. Identifing Functions Work with a partner. Determine whether each relation represents a function. Eplain our reasoning. 8 8 a. Input, Output, b. Input, Output, c. Input, Output, d e. (, 5), (, 8), (, ), (, ), (, 7) f. (, ), (, ), (, ), (, ), (, ), (, ) g. Each radio frequenc in a listening area has eactl one radio station. h. The same television station can be found on more than one channel. i. = j. = + Communicate Your Answer. What is a function? Give eamples of relations, other than those in Eplorations and, that (a) are functions and (b) are not functions. Section. Functions
2 . Lesson Core Vocabular relation, p. function, p. domain, p. range, p. independent variable, p. 7 dependent variable, p. 7 Previous ordered pair mapping diagram What You Will Learn Determine whether relations are functions. Find the domain and range of a function. Identif the independent and dependent variables of functions. Determining Whether Relations Are Functions 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 that pairs each input with eactl one output is a function. Determining Whether Relations Are Functions Determine whether each relation is a function. Eplain. a. (, ), (, ), (, ), (, ), (, ) b. (, ), (8, 7), (, ), (, ), (5, ) c. Input, REMEMBER A relation can be represented b a mapping diagram. d. Output, Input, Output, 5 SOLUTION a. Ever input has eactl one output. So, the relation is a function. b. The input has two outputs, and. So, the relation is not a function. c. The input has two outputs, 5 and. So, the relation is not a function. d. Ever input has eactl one output. So, the relation is a function. Monitoring Progress Help in English and Spanish at BigIdeasMath.com Determine whether the relation is a function. Eplain.. ( 5, ), (, ), (5, ), (5, ). (, 8), (, ), (, ), (5, ). Input, Output,. Input, Output, Chapter Graphing Linear Functions
3 Core Concept Vertical Line Test Words A graph represents a function when no vertical line passes through more than one point on the graph. Eamples Function Not a function Using the Vertical Line Test Determine whether each graph represents a function. Eplain. a. b. SOLUTION a. You can draw a vertical line through (, ) and (, 5). So, the graph does not represent a function. b. No vertical line can be drawn through more than one point on the graph. So, the graph represents a function. Monitoring Progress Help in English and Spanish at BigIdeasMath.com Determine whether the graph represents a function. Eplain Section. Functions 5
4 Finding the Domain and Range of a Function Core Concept The Domain and Range of a Function The domain of a function is the set of all possible input values. The range of a function is the set of all possible output values. input output Finding the Domain and Range from a Graph Find the domain and range of the function represented b the graph. a. b. STUDY TIP A relation also has a domain and a range. SOLUTION a. Write the ordered pairs. Identif the inputs and outputs. inputs (, ), (, ), (, ), (, ) outputs The domain is,,, and. The range is,,, and. b. Identif the - and -values represented b the graph. domain range The domain is. The range is. Monitoring Progress Help in English and Spanish at BigIdeasMath.com Find the domain and range of the function represented b the graph. 9.. Chapter Graphing Linear Functions
5 Identifing Independent and Dependent Variables The variable that represents the input values of a function is the independent variable because it can be an value in the domain. The variable that represents the output values of a function is the dependent variable because it depends on the value of the independent variable. When an equation represents a function, the dependent variable is defined in terms of the independent variable. The statement is a function of means that varies depending on the value of. = + dependent variable, independent variable, Identifing Independent and Dependent Variables The function = + represents the amount (in fluid ounces) of juice remaining in a bottle after ou take gulps. a. Identif the independent and dependent variables. b. The domain is,,,, and. What is the range? SOLUTION a. The amount of juice remaining depends on the number of gulps. So, is the dependent variable, and is the independent variable. b. Make an input-output table to find the range. Input, + Output, () + () + 9 () + () + () + The range is, 9,,, and. Monitoring Progress Help in English and Spanish at BigIdeasMath.com. The function a = b + represents the number a of avocados ou have left after making b batches of guacamole. a. Identif the independent and dependent variables. b. The domain is,,, and. What is the range?. The function t = 9m + 5 represents the temperature t (in degrees Fahrenheit) of an oven after preheating for m minutes. a. Identif the independent and dependent variables. b. A recipe calls for an oven temperature of 5 F. Describe the domain and range of the function. Section. Functions 7
6 . Eercises Dnamic Solutions available at BigIdeasMath.com Vocabular and Core Concept Check. WRITING How are independent variables and dependent variables different?. DIFFERENT WORDS, SAME QUESTION Which is different? Find both answers. Find the range of the function represented b the table. Find the inputs of the function represented b the table. 7 5 Find the -values of the function represented b (, 7), (, 5), and (, ). Find the domain of the function represented b (, 7), (, 5), and (, ). Monitoring Progress and Modeling with Mathematics In Eercises 8, determine whether the relation is a function. Eplain. (See Eample.). (, ), (, ), (, ), (, ), (5, )... (7, ), (5, ), (, 8), (, 5), (, ) 5. Input, Output,. Input, Output, In Eercises, find the domain and range of the function represented b the graph. (See Eample.).. 7. Input, Output, 8. Input, 9 Output, In Eercises 9, determine whether the graph represents a function. Eplain. (See Eample.) MODELING WITH MATHEMATICS The function = represents our monthl rent (in dollars) when ou pa das late. (See Eample.) a. Identif the independent and dependent variables. b. The domain is,,,,, and 5. What is the range? 8 Chapter Graphing Linear Functions
7 8. MODELING WITH MATHEMATICS The function = represents the cost (in dollars) of a tai ride of miles.. MULTIPLE REPRESENTATIONS The function = represents the number of hardcover books and softcover books ou can bu at a used book sale. a. Solve the equation for. b. Make an input-output table to find ordered pairs for the function. c. Plot the ordered pairs in a coordinate plane. 5. ATTENDING TO PRECISION The graph represents a function. Find the input value corresponding to an output of. a. Identif the independent and dependent variables. b. You have enough mone to travel at most miles in the tai. Find the domain and range of the function. ERROR ANALYSIS In Eercises 9 and, describe and correct the error in the statement about the relation shown in the table.. OPEN-ENDED Fill in the table so that when t is the 9.. Input, 5 Output, The relation is not a function. One output is paired with two inputs. independent variable, the relation is a function, and when t is the dependent variable, the relation is not a function. t v 7. ANALYZING RELATIONSHIPS You select items in a vending machine b pressing one letter and then one number. The relation is a function. The range is,,,, and 5. ANALYZING RELATIONSHIPS In Eercises and, identif the independent and dependent variables.. The number of quarters ou put into a parking meter affects the amount of time ou have on the meter.. The batter power remaining on our MP plaer is based on the amount of time ou listen to it.. MULTIPLE REPRESENTATIONS The balance (in dollars) of our savings account is a function of the month. Month, Balance (dollars), a. Describe this situation in words. a. Eplain wh the relation that pairs letter-number combinations with food or drink items is a function. b. Write the function as a set of ordered pairs. b. Identif the independent and dependent variables. c. Plot the ordered pairs in a coordinate plane. c. Find the domain and range of the function. Section. hsnb_alg_pe_.indd 9 Functions 9 //5 :8 PM
8 8. HOW DO YOU SEE IT? The graph represents the height h of a projectile after t seconds. Height (feet) Height of a Projectile 5 h t Time (seconds) a. Eplain wh h is a function of t. b. Approimate the height of the projectile after.5 second and after.5 seconds. c. Approimate the domain of the function. d. Is t a function of h? Eplain.. A function pairs each chaperone on a school trip with students. REASONING In Eercises 5 8, tell whether the statement is true or false. If it is false, eplain wh. 5. Ever function is a relation.. Ever relation is a function. 7. When ou switch the inputs and outputs of an function, the resulting relation is a function. 8. When the domain of a function has an infinite number of values, the range alwas has an infinite number of values. 9. MATHEMATICAL CONNECTIONS Consider the triangle shown. 9. MAKING AN ARGUMENT Your friend sas that a line alwas represents a function. Is our friend correct? Eplain. h. THOUGHT PROVOKING Write a function in which the inputs and/or the outputs are not numbers. Identif the independent and dependent variables. Then find the domain and range of the function. ATTENDING TO PRECISION In Eercises, determine whether the statement uses the word function in a wa that is mathematicall correct. Eplain our reasoning.. The selling price of an item is a function of the cost of making the item.. The sales ta on a purchased item in a given state is a function of the selling price.. A function pairs each student in our school with a homeroom teacher. Maintaining Mathematical Proficienc Write the sentence as an inequalit. (Section.) a. Write a function that represents the perimeter of the triangle. b. Identif the independent and dependent variables. c. Describe the domain and range of the function. (Hint: The sum of the lengths of an two sides of a triangle is greater than the length of the remaining side.) REASONING In Eercises, find the domain and range of the function.. =. =. =. =. A number is less than. 5. Three is no less than a number.. Seven is at most the quotient of a number d and The sum of a number w and is more than. Reviewing what ou learned in previous grades and lessons Evaluate the epression. (Skills Review Handbook) ( ) Chapter Graphing Linear Functions
Functions. 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 informationEssential Question How can you solve a system of linear equations? $15 per night. Cost, C (in dollars) $75 per Number of. Revenue, R (in dollars)
5.1 Solving Sstems of Linear Equations b Graphing Essential Question How can ou solve a sstem of linear equations? Writing a Sstem of Linear Equations Work with a partner. Your famil opens a bed-and-breakfast.
More informationLinear Functions. Essential Question How can you determine whether a function is linear or nonlinear?
. Linear Functions Essential Question How can ou determine whether a function is linear or nonlinear? Finding Patterns for Similar Figures Work with a partner. Cop and complete each table for the sequence
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 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 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 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 informationEssential Question How can you use a scatter plot and a line of fit to make conclusions about data?
. Scatter Plots and Lines of Fit Essential Question How can ou use a scatter plot and a line of fit to make conclusions about data? A scatter plot is a graph that shows the relationship between two data
More informationEssential Question How can you use a quadratic function to model a real-life situation?
3. TEXAS ESSENTIAL KNOWLEDGE AND SKILLS A..A A..E A..A A..B A..C Modeling with Quadratic Functions Essential Question How can ou use a quadratic function to model a real-life situation? Work with a partner.
More informationFactoring Polynomials
5. TEXAS ESSENTIAL KNOWLEDGE AND SKILLS 2A.7.D 2A.7.E Factoring Polnomials Essential Question How can ou factor a polnomial? Factoring Polnomials Work with a partner. Match each polnomial equation with
More informationSolving Equations with Variables on Both Sides
1. Solving Equations with Variables on Both Sides Essential Question How can you solve an equation that has variables on both sides? Perimeter Work with a partner. The two polygons have the same perimeter.
More informationCharacteristics of Quadratic Functions
. Characteristics of Quadratic Functions Essential Question What tpe of smmetr does the graph of f() = a( h) + k have and how can ou describe this smmetr? Parabolas and Smmetr Work with a partner. a. Complete
More information(0, 2) y = x 1 2. y = x (2, 2) y = 2x + 2
. TEXAS ESSENTIAL KNOWLEDGE AND SKILLS G..B G..C Equations of Parallel and Perpendicular Lines Essential Question How can ou write an equation of a line that is parallel or perpendicular to a given line
More informationMaintaining Mathematical Proficiency
Name Date Chapter 3 Maintaining Mathematical Proficienc Plot the point in a coordinate plane. Describe the location of the point. 1. A( 3, 1). B (, ) 3. C ( 1, 0). D ( 5, ) 5. Plot the point that is on
More informationChapter 3. 2, which matches a typical. Worked-Out Solutions. Chapter 3 Maintaining Mathematical Proficiency (p.101)
Chapter Chapter Maintaining Mathematical Proficienc (p.). C A B E F D. This point is in Quadrant I.. This point is in Quadrant II.. This point is on the positive -ais.. This point is in Quadrant III. 5.
More informationEssential Question How can you determine the number of solutions of a linear system?
.1 TEXAS ESSENTIAL KNOWLEDGE AND SKILLS A.3.A A.3.B Solving Linear Sstems Using Substitution Essential Question How can ou determine the number of solutions of a linear sstem? A linear sstem is consistent
More informationModeling with Exponential and Logarithmic Functions 6.7. Essential Question How can you recognize polynomial, exponential, and logarithmic models?
.7 Modeling with Eponential and Logarithmic Functions Essential Question How can ou recognize polnomial, eponential, and logarithmic models? Recognizing Different Tpes of Models Work with a partner. Match
More informationMaintaining Mathematical Proficiency
Name Date Chapter 5 Maintaining Mathematical Proficienc Graph the equation. 1. + =. = 3 3. 5 + = 10. 3 = 5. 3 = 6. 3 + = 1 Solve the inequalit. Graph the solution. 7. a 3 > 8. c 9. d 5 < 3 10. 8 3r 5 r
More informationSolving Systems of Linear Equations
5 Solving Sstems of Linear Equations 5. Solving Sstems of Linear Equations b Graphing 5. Solving Sstems of Linear Equations b Substitution 5.3 Solving Sstems of Linear Equations b Elimination 5. Solving
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 informationSolving Linear Systems
1.4 Solving Linear Sstems Essential Question How can ou determine the number of solutions of a linear sstem? A linear sstem is consistent when it has at least one solution. A linear sstem is inconsistent
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 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 information4 B. 4 D. 4 F. 3. How can you use the graph of a quadratic equation to determine the number of real solutions of the equation?
3.1 Solving Quadratic Equations COMMON CORE Learning Standards HSA-SSE.A. HSA-REI.B.b HSF-IF.C.8a Essential Question Essential Question How can ou use the graph of a quadratic equation to determine the
More informationExponential and Logarithmic Functions
Eponential and Logarithmic Functions.1 Eponential Growth and Deca Functions. The Natural Base e.3 Logarithms and Logarithmic Functions. Transformations of Eponential and Logarithmic Functions.5 Properties
More information4.4 Scatter Plots and Lines of Fit 4.5 Analyzing Lines of Fit 4.6 Arithmetic Sequences 4.7 Piecewise Functions
Writing Linear Functions. Writing Equations in Slope-Intercept Form. Writing Equations in Point-Slope Form.3 Writing Equations of Parallel and Perpendicular Lines. Scatter Plots and Lines of Fit.5 Analzing
More informationEssential Question How can you use substitution to solve a system of linear equations?
5.2 Solving Systems of Linear Equations by Substitution Essential Question How can you use substitution to solve a system of linear equations? Using Substitution to Solve Systems Work with a partner. Solve
More informationSpecial Right Triangles
. Special Right Triangles Essential Question What is the relationship among the side lengths of - - 0 triangles? - - 0 triangles? Side Ratios of an Isosceles Right Triangle ATTENDING TO PRECISION To be
More informationEssential Question How can you determine whether a polynomial equation has imaginary solutions? 2 B. 4 D. 4 F.
5. TEXAS ESSENTIAL KNOWLEDGE AND SKILLS 2A.7.A The Fundamental Theorem of Algebra Essential Question How can ou determine whether a polnomial equation has imaginar solutions? Cubic Equations and Imaginar
More informationName Date. and y = 5.
Name Date Chapter Fair Game Review Evaluate the epression when = and =.... 0 +. 8( ) Evaluate the epression when a = 9 and b =.. ab. a ( b + ) 7. b b 7 8. 7b + ( ab ) 9. You go to the movies with five
More informationInverse of a Function
. Inverse o a Function Essential Question How can ou sketch the graph o the inverse o a unction? Graphing Functions and Their Inverses CONSTRUCTING VIABLE ARGUMENTS To be proicient in math, ou need to
More informationSystems of Linear Inequalities
. Sstems of Linear Inequalities sstem of linear inequalities? How can ou sketch the graph of a ACTIVITY: Graphing Linear Inequalities Work with a partner. Match the linear inequalit with its graph. + Inequalit
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 informationEssential Question How can you solve an absolute value inequality? Work with a partner. Consider the absolute value inequality x
Learning Standards HSA-CED.A.1 HSA-REI.B.3.6 Essential Question How can you solve an absolute value inequality? COMMON CORE Solving an Absolute Value Inequality Algebraically MAKING SENSE OF PROBLEMS To
More informationMultiplying and Dividing Rational Expressions
6.3 Multiplying and Dividing Rational Epressions Essential Question How can you determine the ecluded values in a product or quotient of two rational epressions? You can multiply and divide rational epressions
More informationSEE the Big Idea. Quonset Hut (p. 218) Zebra Mussels (p. 203) Ruins of Caesarea (p. 195) Basketball (p. 178) Electric Vehicles (p.
Polnomial Functions.1 Graphing Polnomial Functions. Adding, Subtracting, and Multipling Polnomials.3 Dividing Polnomials. Factoring Polnomials.5 Solving Polnomial Equations. The Fundamental Theorem of
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 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 informationEssential Question How can you find a trigonometric function of an acute angle θ? opp. hyp. opp. adj. sec θ = hyp. adj.
. Right Triangle Trigonometry Essential Question How can you find a trigonometric function of an acute angle? Consider one of the acute angles of a right triangle. Ratios of a right triangle s side lengths
More information1.3 Exercises. Vocabulary and Core Concept Check. Dynamic Solutions available at BigIdeasMath.com
1.3 Eercises Dnamic Solutions available at BigIdeasMath.com Vocabular and Core Concept Check 1. COMPLETE THE SENTENCE The linear equation = 1 + 3 is written in form.. VOCABULARY A line of best fit has
More informationSolving Quadratic Equations
9 Solving Quadratic Equations 9. Properties of Radicals 9. Solving Quadratic Equations b Graphing 9. Solving Quadratic Equations Using Square Roots 9. Solving Quadratic Equations b Completing the Square
More informationACTIVITY: Using a Table to Plot Points
.5 Graphing Linear Equations in Standard Form equation a + b = c? How can ou describe the graph of the ACTIVITY: Using a Table to Plot Points Work with a partner. You sold a total of $6 worth of tickets
More informationBIG IDEAS MATH. Ron Larson Laurie Boswell. Sampler
BIG IDEAS MATH Ron Larson Laurie Boswell Sampler 3 Polnomial Functions 3.1 Graphing Polnomial Functions 3. Adding, Subtracting, and Multipling Polnomials 3.3 Dividing Polnomials 3. Factoring Polnomials
More information2.3 Start Thinking. 2.3 Warm Up. 2.3 Cumulative Review Warm Up
. Start Thinking Choose an two numbers and compare them with an inequalit smbol ( < or > ). Multipl each number b 1. Is the new inequalit still true? Continue this eercise b dividing the original inequalit
More informationFunctions. Essential Question What are some of the characteristics of the graph of a logarithmic function?
5. Logarithms and Logarithmic Functions Essential Question What are some o the characteristics o the graph o a logarithmic unction? Ever eponential unction o the orm () = b, where b is a positive real
More informationEssential Question How can you use a rational exponent to represent a power involving a radical?
5.1 nth Roots and Rational Exponents Essential Question How can you use a rational exponent to represent a power involving a radical? Previously, you learned that the nth root of a can be represented as
More informationMaintaining Mathematical Proficiency
Name Date Chapter 8 Maintaining Mathematical Proficienc Graph the linear equation. 1. = 5. = + 3 3. 1 = + 3. = + Evaluate the epression when =. 5. + 8. + 3 7. 3 8. 5 + 8 9. 8 10. 5 + 3 11. + + 1. 3 + +
More informationUnit 2: Linear Equations and Inequalities
Mr. Thurlwell's Assignment Sheet Algebra 1 Unit 2: Linear Equations and Inequalities Name: Assignment #1 (3.3) pg 177 4-22e Assignment #2 (4.3) pg 235 2-10e, 24,30,47,50 Assignment #3 (4.1) pg 219 2-14e,15,59
More information2.0 % annual 3.0 % Quiz. CD Specials
6.1 6. Quiz Tell whether the function represents eponential growth or eponential deca. Eplain our reasoning. (Sections 6.1 and 6.) 1. f () = (.5). = ( 3 8) Simplif the epression. (Sections 6. and 6.3)
More informationInequalities and Multiplication
Lesson 3-6 Inequalities and Multiplication BIG IDEA Multipling each side of an inequalit b a positive number keeps the direction of the inequalit; multipling each side b a negative number reverses the
More informationRational Exponents and Radical Functions
.1..... Rational Eponents and Radical Functions nth Roots and Rational Eponents Properties of Rational Eponents and Radicals Graphing Radical Functions Solving Radical Equations and Inequalities Performing
More informationExponential and Logarithmic Functions
7 Eponential and Logarithmic Functions 7.1 Eponential Growth and Deca Functions 7. The Natural Base e 7.3 Logarithms and Logarithmic Functions 7. Transformations of Eponential and Logarithmic Functions
More informationSummary and Vocabulary
Chapter Chapter Summar and Vocabular Equations involving percents ma be written in the form p q = r, where p is the decimal form of the percent, q is the initial quantit, and r is the resulting quantit.
More informationChapter Start Thinking! For use before Activity 6.1. For use before Activity Start Thinking! For use before Lesson
. Enrichment and Etension. a =, b =. a =, b =. a =, b =. a =, b =. a =, b is an number ecept.. a =, b =. a =, b =. a =, b =. Check students work.. Puzzle PAY HIM Etension. Start Thinking! For use before
More informationEssential Question How can you verify a trigonometric identity?
9.7 Using Trigonometric Identities Essential Question How can you verify a trigonometric identity? Writing a Trigonometric Identity Work with a partner. In the figure, the point (, y) is on a circle of
More informationDomain, Range, and End Behavior
Locker LESSON 1.1 Domain, Range, and End Behavior Common Core Math Standards The student is epected to: F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship
More informationEssential Question How can you cube a binomial? Work with a partner. Find each product. Show your steps. = (x + 1) Multiply second power.
4.2 Adding, Subtracting, and Multiplying Polynomials COMMON CORE Learning Standards HSA-APR.A.1 HSA-APR.C.4 HSA-APR.C.5 Essential Question How can you cube a binomial? Cubing Binomials Work with a partner.
More informationMaintaining Mathematical Proficiency
Chapter Maintaining Mathematical Proficienc Find the -intercept of the graph of the linear equation. 1. = + 3. = 3 + 5 3. = 10 75. = ( 9) 5. 7( 10) = +. 5 + 15 = 0 Find the distance between the two points.
More information1Write and graph. 2Solve problems. Now. Then. Why? New Vocabulary
Direct Variation Then You found rates of change of linear functions. (Lesson -) Now Write and graph direct variation equations. Solve problems involving direct variation. Wh? Bianca is saving her mone
More informationSolving Exponential and Logarithmic Equations
5.5 Solving Exponential and Logarithmic Equations Essential Question How can ou solve exponential and logarithmic equations? Solving Exponential and Logarithmic Equations Work with a partner. Match each
More informationSolving Polynomial Equations 3.5. Essential Question How can you determine whether a polynomial equation has a repeated solution?
3. Solving Polynomial Equations Essential Question Essential Question How can you determine whether a polynomial equation has a repeated solution? Cubic Equations and Repeated Solutions USING TOOLS STRATEGICALLY
More informationDiscrete and Continuous Domains
. Discrete and Continuous Domains How can ou decide whether the domain of a function is discrete or continuous? EXAMPLE: Discrete and Continuous Domains In Activities and in Section., ou studied two real-life
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 information3.1 Start Thinking. 3.1 Warm Up. 3.1 Cumulative Review Warm Up. Consider the equation y = x.
3.1 Start Thinking Consider the equation =. Are there an values of that ou cannot substitute into the equation? If so, what are the? Are there an values of that ou cannot obtain as an answer? If so, what
More informationTOPIC ESSENTIAL QUESTION
TOPIC Topic Review TOPIC ESSENTIAL QUESTION 1. How can linear functions be used to model situations and solve problems? Vocabular Review Choose the correct term to complete each sentence.. When tends to
More information74 Maths Quest 10 for Victoria
Linear graphs Maria is working in the kitchen making some high energ biscuits using peanuts and chocolate chips. She wants to make less than g of biscuits but wants the biscuits to contain at least 8 g
More informationLaurie s Notes. Overview of Section 2.4
Overview of Section 2. Introduction The goal in this lesson is for students to create quadratic equations to represent the relationship between two quantities (HSA-CED.A.2). From the contet given, students
More informationAlgebra I Notes Direct Variation Unit 04e
OBJECTIVES: F.IF.B.4 Interpret functions that arise in applications in terms of the contet. For a function that models a relationship between two quantities, interpret ke features of graphs and tables
More informationSolving Systems of Linear Equations by Graphing
. Solving Sstems of Linear Equations b Graphing How can ou solve a sstem of linear equations? ACTIVITY: Writing a Sstem of Linear Equations Work with a partner. Your famil starts a bed-and-breakfast. The
More informationEssential Question How can you factor a polynomial completely?
REASONING ABSTRACTLY 7.8 To be proficient in math, ou need to know and flexibl use different properties of operations and objects. Factoring Polnomials Completel Essential Question How can ou factor a
More informationFair Game Review. Chapter of a mile the next day. How. far will you jog over the next two days? How many servings does the
Name Date Chapter Evaluate the epression.. Fair Game Review 5 +. 3 3 7 3 8 4 3. 4 4. + 5 0 5 6 5. 3 6. 4 6 5 4 6 3 7. 5 8. 3 9 8 4 3 5 9. You plan to jog 3 4 of a mile tomorrow and 7 8 of a mile the net
More informationAnalyzing Lines of Fit
4.5 Analyzing Lines of Fit Essential Question How can you analytically find a line of best fit for a scatter plot? Finding a Line of Best Fit Work with a partner. The scatter plot shows the median ages
More informationElementary Algebra ~ Review for Exam 2
Elementar Algebra ~ Review for Eam 2 Solve using the five-step problem-solving process. 1) The second angle of a triangle is 3 times as large as the first. The third angle is 3e more than the first. Find
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 informationGraphing and Writing Linear Equations
Graphing and Writing Linear Equations. Graphing Linear Equations. Slope of a Line. Graphing Linear Equations in Slope-Intercept Form. Graphing Linear Equations in Standard Form. Writing Equations in Slope-Intercept
More informationWhat You ll Learn Identify direct variation. Use direct variation to solve problems.
AM_S_C_L_3.indd Page // 3: PM s-user /Volumes//GO/CORE_READING/TENNESSEE/ANCILLARY... Proportionalit and Linear Relationships Teach the Concept Lesson - Direct Variation Interactive Stud Guide See pages
More informationBridge-Thickness Experiment. Student 2
Applications 1. Below are some results from the bridge-thickness eperiment. Bridge-Thickness Eperiment Thickness (laers) Breaking Weight (pennies) 15 5 5 a. Plot the (thickness, breaking weight) data.
More informationSystems of Linear Equations
Sstems of Linear Equations Monetar Sstems Overload Lesson 3-1 Learning Targets: Use graphing, substitution, and elimination to solve sstems of linear equations in two variables. Formulate sstems of linear
More informationFair Game Review. Chapter = How many calculators are sold when the profit is $425? Solve the equation. Check your solution.
Name Date Chapter 4 Fair Game Review Solve the equation. Check our solution.. 8 3 = 3 2. 4a + a = 2 3. 9 = 4( 3k 4) 7k 4. ( m) 2 5 6 2 = 8 5. 5 t + 8t = 3 6. 3 5h 2 h + 4 = 0 2 7. The profit P (in dollars)
More informationHow can you construct and interpret a scatter plot? ACTIVITY: Constructing a Scatter Plot
9. Scatter Plots How can ou construct and interpret a scatter plot? ACTIVITY: Constructing a Scatter Plot Work with a partner. The weights (in ounces) and circumferences C (in inches) of several sports
More informationIntroduction Direct Variation Rates of Change Scatter Plots. Introduction. EXAMPLE 1 A Mathematical Model
APPENDIX B Mathematical Modeling B1 Appendi B Mathematical Modeling B.1 Modeling Data with Linear Functions Introduction Direct Variation Rates of Change Scatter Plots Introduction The primar objective
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C)b = h 2A
MATH 830/GRACEY EXAM PRACTICE/CH..-3 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the formula for the specified variable. 1) A = 1 bh
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 informationName Class Date. Inverse of Function. Understanding Inverses of Functions
Name Class Date. Inverses of Functions Essential Question: What is an inverse function, and how do ou know it s an inverse function? A..B Graph and write the inverse of a function using notation such as
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 information5.7 Start Thinking. 5.7 Warm Up. 5.7 Cumulative Review Warm Up
.7 Start Thinking Graph the linear inequalities < + and > 9 on the same coordinate plane. What does the area shaded for both inequalities represent? What does the area shaded for just one of the inequalities
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 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 information8.4. If we let x denote the number of gallons pumped, then the price y in dollars can $ $1.70 $ $1.70 $ $1.70 $ $1.
8.4 An Introduction to Functions: Linear Functions, Applications, and Models We often describe one quantit in terms of another; for eample, the growth of a plant is related to the amount of light it receives,
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 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 informationYou studied exponential growth and decay functions.
TEKS 7. 2A.4.B, 2A..B, 2A..C, 2A..F Before Use Functions Involving e You studied eponential growth and deca functions. Now You will stud functions involving the natural base e. Wh? So ou can model visibilit
More informationSystems of Linear Equations
Sstems of Linear Equations Monetar Sstems Overload Lesson 3-1 Learning Targets: Use graphing, substitution, and elimination to solve sstems of linear equations in two variables. Formulate sstems of linear
More informationx. 4. 2x 10 4x. 10 x
CCGPS UNIT Semester 1 COORDINATE ALGEBRA Page 1 of Reasoning with Equations and Quantities Name: Date: Understand solving equations as a process of reasoning and eplain the reasoning MCC9-1.A.REI.1 Eplain
More informationUsing Graphs to Relate Two Quantities
- Using Graphs to Relate Two Quantities For Eercises, choose the correct letter.. The graph shows our distance from the practice field as ou go home after practice. You received a ride from a friend back
More informationSkills Practice Skills Practice for Lesson 5.1
Skills Practice Skills Practice for Lesson. Name Date Widgets, Dumbbells, and Dumpsters Multiple Representations of Linear Functions Vocabular Write the term that best completes each statement.. A(n) is
More informationHow can you use multiplication or division to solve an inequality? ACTIVITY: Using a Table to Solve an Inequality
. Solving Inequalities Using Multiplication or Division How can you use multiplication or division to solve an inequality? 1 ACTIVITY: Using a Table to Solve an Inequality Work with a partner. Copy and
More informationApplications. 60 Say It With Symbols. g = 25 -
Applications 1. A pump is used to empt a swimming pool. The equation w =-275t + 1,925 represents the gallons of water w that remain in the pool t hours after pumping starts. a. How man gallons of water
More informationChapter 9 BUILD YOUR VOCABULARY
C H A P T E R 9 BUILD YUR VCABULARY Chapter 9 This is an alphabetical list of new vocabular terms ou will learn in Chapter 9. As ou complete the stud notes for the chapter, ou will see Build Your Vocabular
More informationFair Game Review. Chapter 2. and y = 5. Evaluate the expression when x = xy 2. 4x. Evaluate the expression when a = 9 and b = 4.
Name Date Chapter Fair Game Review Evaluate the epression when = and =.... 0 +. 8( ) Evaluate the epression when a = 9 and b =.. ab. a ( b + ) 7. b b 7 8. 7b + ( ab ) 9. You go to the movies with five
More information