Linear Functions Unit Table Of Contents - Weebly
Linear Functions Unit Table of ContentsUnit Scope and Sequence .Page 1Day 1 Summary Page 3 Diversity promoted through story problems Instructional Strategies: have students work in pairs or small groups; adjusted level ofdifficultyDay 2 Detailed .Page 9 Interdisciplinary: Science and Math Instructional Strategy: provide resource sheetDay 3 Summary Page 20Day 4 Summary Page 24Day 5 Summary Page 29 Interdisciplinary: English and Matho Rubric provided Diversity promoted on the handout Quiz with rubric Instructional Strategy: clarify expectations with a rubricDay 6 Summary Page 36 Technology used: iPad or Laptop for each studentDay 7 Detailed .Page 40 Instructional Strategies: reduce amount of copying (by providing resource sheet)Day 8 Summary Page 46 Instructional Strategies: use multiple representations; offer manipulativesDay 9 Summary Page 51Day 10 Summary .Page 54 Instructional Strategies: teach and model strategies for organization and studying; providestudy guides with key informationDay 11 Summary .Page 57 Test: sample questions providedBibliography .Page 60
1Unit Plan Scope and SequenceMelanie LeonardTitle: Linear FunctionsGrade Level: 8th GradeSubject: Algebra IUnit Calendar:Day 1: Graphing equations Students will review coordinate planes and how to plot points Students will be given equations in y mx b form and be asked to make a table Students will plot the points from their table Students will use their graphs to answer story problems Students will learn the terms linear and y-intercept and how to interpret y-intercept in astory problemDay 2: Functions Students will define a function and learn function notation (ie: f(x)) Students will learn the vertical line test Students will practice identifying functions with linear and nonlinear functionsDay 3: Analyzing linear equations Students will learn the term slope Students will learn how to identify slope from a graph (first a positive slope, then anegative slope, then a zero slope)Day 4: Analyzing slope and slope-intercept form Students will learn to recognize slope from a linear equation and learn the terms directvariation and constant of variation with equations in the form y kx (first k 0, thenequations where k 0, then equations where k is a fraction) Students will move on to slope-intercept form (y mx b) and interpret the slope from theequation Students will compare parallel slopes and perpendicular slopesDay 5: Writing equations in slope-intercept form Quiz on analyzing linear equations Students will be given a point and slope and will write an equation in the form y mx b Students will be given two points and will calculate the slope, then write the equation iny mx b formDay 6: Writing equations in other forms Students will be introduced to standard form and point-slope form Given a point and a slope, students will be asked to write an equation in all three forms Given two points, students will be asked to write an equation in all three formsDay 7: Graphing systems of equations Students will graph two linear equations and be introduced to the idea of systems ofequations Students will learn key terminology (consistent, inconsistent, independent, anddependent) and will learn the three categories for solving a system of equations:
2intersecting lines (one solution), same line (infinite solutions), or parallel lines (nosolution) Students will use graphs to solve systems of equationsDay 8: Solving systems of equations with substitution Students will learn the substitution method for solving systems of equations First, students will work with systems that have one solution (first using equations solvedfor a variable, then using equations where they have to solve for a variable beforestarting) Next, students will look at systems with infinite solutions, then systems with no solutionsDay 9: Solving systems of equations with elimination Students will learn the elimination method for solving systems of equations Students will begin with equations in standard form that can be added or subtracted Students will use equations in different forms that can be added or subtracted Students will be given equations that first need to be multiplied by a scalar, then added orsubtractedDay 10: Review and application Students will review the concepts covered in the linear functions unit Students will practice applying these concepts to story problems and real-world contextsDay 11: Test Students will take a test on writing linear equations and solving systems of equationsBig Ideas: Students will know How to graph equations on a coordinate planeHow to interpret slope and y-intercept from linear equations in standard form, slope-interceptform, and point-slope formHow to solve systems of equations using graphs, substitution, and eliminationRational:By completing this unit, students will fulfill 8th grade common core standards for functions as well as highschool standards for algebra and functions. In addition, a unit on linear functions lays the groundwork forharder functions, such as quadratic, cubic, or trigonometric functions, which are harder to write andinterpret. With this base of knowledge, students will be able to succeed in the rest of this algebra courseas well as in higher level high school and college math courses.
3Linear FunctionsDay 1—Graphing Linear EquationsEssential Question: How do we graph linear equations and how can we use those graphs?Common Core/Objective: CCSS.Math.Content.8.F.A.3 Interpret the equation y mx b as defining a linearfunction, whose graph is a straight line; give examples of functions that are not linear. Objective: I can plot points from a linear equation and interpret those points.Warm Up – Activates Prior Knowledge—5 minutes: Students will be given a worksheet with blank coordinate planes and coordinate planeswith several points. Students will have to plot points on the blank planes and identify thepoints on the other coordinate planes (page 5). Rational: This activity will activate students’ prior knowledge of plotting points. Inaddition, the worksheet will have some linear plots and some nonlinear plots, which willserve as an introduction to identifying linear equations in this lesson.Preparation/Materials: Students: Textbook (Algebra I: Glencoe Mathematics Michigan Edition), graph paper toplot points as the teacher gives examples and for plotting graphs during the active lesson,notebook, pencil Teacher: Copies of warm up worksheet for each student, warm up answer key, extragraph paper for students who need it, note cards with story problems and correspondinglinear equations, projector/PowerPoint to display all examples for students. Advanced Preparation: Create the note card problems with different levels of difficulty inorder to differentiate instruction (first: positive slope, second: negative slope, third:common fractions, fourth: uncommon fractions, fifth: equations not in the formy mx b). Make sure that you give tables a note card with an appropriate level ofdifficulty (you may want to color code the note cards so it is easy to tell which is which).When writing out the story problems, make the characters and situations ethnicallydiverse.Vocabulary Development: Terms: coordinate plane, quadrant, graph, linear, y-intercept These terms will be introduced at the beginning of the lesson as well as used throughoutthe lesson so that students can learn their meaning through the context of their use.Skill Lesson through direct instruction and modeling—10-15 minutes: Teacher will go over the warm up, which will lead in to introducing the vocabulary. Thewarm up examples will serve as examples for linear vs. nonlinear graphs. Teacher will model creating a table from an equation in the form y mx b, then plot thepoints. Students will follow along with the plotting on their own graph paper. Theteacher will model how to find the y-intercept.
4 Teacher will model a second equation coming from the context of a story problem: howmany calories are burned in a certain amount of time (page 220 in the textbook). Withthe given equation, the class will construct a table and graph. Then the teacher will askhow many calories were burned at a time not listed in the table. Students will try toanswer this on their own before the teacher models how to estimate using a graph. Theteacher will also ask students to explain what they think the y-intercept means in thecontext of the story problem.Rational: The easiest and most common way for students to see linear equations is in theform y mx b. By using this form of equation, we are laying the ground work forstudents to identify slope and y-intercept from the equation. During the story problemexample, students are given the chance to solve the problem before the teacher shares hermethod because this encourages inquiry-based learning.Active Lesson (problem solving reasoning / critical thinking / student led) 20 minutes: Students will work in their table groups. The teacher will give each table a story problemon a notecard that includes a linear equation in the form y mx b, and a question thatstudents will have to answer with their graphs. Groups will have to create a table with atleast 5 values, then plot their points and use the graph to estimate a solution to thequestion. Students will then call the teacher over and explain the answer to their questionand what the y-intercept means in this context. The teacher will then give the groupanother note card. Rational: The teacher can differentiate instruction with the note cards. Some linearequations will have “nice” numbers while others will include fractions. All students willstart with an increasing function, but as students master that, the note cards will startrepresenting situations where the equation has a negative slope. The note card a tablereceives will depend on the level that table is at. For extension on this topic, an advancedtable would receive a note card with an equation in standard form (ax by c). Studentswill have to call on their prior knowledge to solve for y, then complete the problem.Assessment: Formative: as students are working, the teacher will walk around the room and observeprogress as students are working. In addition, depending on which note card students areusing, the teacher can tell how quickly students are mastering the material.Last 5 minutes: Teacher will collect the note cards and assign the homework (see page 7), which willemphasis the concepts in this lesson that the student should be taking away. If time,students may work on their homework during this time. Rational: The homework gives students extra practice on the new skills they havelearned. In addition, thinking about mathematical concepts outside of class will helpstudents remember the material. I have made up this worksheet in order to assess thematerial that students should know after the lesson. The application problem came fromthe textbook, but I modified it by asking students to explain what the y-intercept means inthe context of the story problem. This shows how well students are conceptuallyunderstanding the material, and it also lays the groundwork for fulfilling common corestandards for high school, which ask students to interpret functions in a given context.
5Warm UpDay 1Plot these points on the grid below:(-2, 4); (-1, 1); (0,0); (1, 1); (2, 4)Plot these points on the grid below:(0, 0); (1,2); (2, 4); (3, 6); (4, 8)Identify the points plotted below:Identify the points plotted below:((,); (,); (,); (,),); (,); (,); (,)
6Warm Up KEYDay 1Plot these points on the grid below:(0, 0); (1,2); (2, 4); (3, 6); (4, 8)Plot these points on the grid below:(-2, 4); (-1, 1); (0,0); (1, 1); (2, 4)Identify the points plotted below:Identify the points plotted below:(-4,-6); (-2,-2); (0, 2); (2, 6)(-4, 6); (1, 2); (3, -4); (7, -6)
7Last 5 Minutes (Homework)Day 1Circle the linear graphs:Application:A taxi company charges a fare of 2.25 plus 0.75 per mile traveled. The cost of the fare c can bedescribed by the equation c 0.75m 2.25 where m is the number of miles traveled.a) On a separate piece of graph paper, make a table with at least 5 values for this equation, thenmake a graph that goes up to at least 20 miles.b) If you need to travel 18 miles, how much will the taxi fare cost? Use your graph to estimate.c) What is the value of the y-intercept in this problem? Explain what the y-intercept means inthe context of the story problem.
8Last 5 Minutes (Homework) KEYDay 1Circle the linear graphs:Application:A taxi company charges a fare of 2.25 plus 0.75 per mile traveled. The cost of the fare c can bedescribed by the equation c 0.75m 2.25 where m is the number of miles traveled.a) On a separate piece of graph paper, make a table with at least 5 values for this equation, thenmake a graph that goes up to at least 20 miles.b) If you need to travel 18 miles, how much will the taxi fare cost? Use your graph to estimate. 15.75c) What is the value of the y-intercept in this problem? Explain what the y-intercept means inthe context of the story problem.The y-intercept is 2.25. It means that before you travel any miles, you have to pay a feeof 2.25.
9Linear Functions—Day 2 Detailed Lesson PlanTeachers: Melanie LeonardSubject Area: Algebra IGrade Level: 8thUnit Title: Linear FunctionsLesson Title: What is a function?Common Core Standards: CCSS.Math.Content.8.F.A.1 Understand that a function is a rule thatassigns to each input exactly one output. The graph of a function is the set of ordered pairsconsisting of an input and the corresponding output. CCSS.Math.Content.8.F.A.3 Interpret theequation y mx b as defining a linear function, whose graph is a straight line; give examples offunctions that are not linear. CCSS.Math.Content.HSF-IF.A.1 Understand that a function from oneset (called the domain) to another set (called the range) assigns to each element of the domainexactly one element of the range. If f is a function and x is an element of its domain, then f(x)denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y f(x). CCSS.Math.Content.HSF-IF.A.2 Use function notation, evaluate functions for inputs in theirdomains, and interpret statements that use function notation in terms of a context.NCTM Standards / 8 Mathematical Practices (check & provide rationale for all that apply) Problem Solving(1)Students will have to think critically about how two quantities relateto each other during the stations activity. In addition, students will be problem solving intheir homework to determine the value of a function at a given input, Reasoning/Proof(2, 8) Click here to enter text., Communication(3)Students will be communicating and working with each other duringthe stations activity, Connections / Representation (4) Students will use the objects at each station to representfunctions. During this process, they will be relating their concepts of scientific experimentsto their mathematical knowledge, Strategic tools(5)Students will use a resource page to take notes, which will help themstay organized and engaged, Precision(6 Click here to enter text.) and structure(7)Click here to enter text.Materials/Resources Needed: Students: pencils, notebooks. Teachers: projector/PowerPoint todisplay warm up, warm up answer key, answers to last night’s homework, copies of resource pagefor each student, copies of the stations packet for each student. At Stations: pencils/rulers, zip lockbags attached to rubber bands and rocks, a timer and a set of Jenga blacks, circle cut-outs ofdifferent sizes and beads to lay on top of the circle cut-outs.Anticipatory Set / Warm up (List specific statements or activities you will use to focus studentson the lesson for the day): 5 minutes: Students will be given an equation in the form y mx b
10and will be asked to make a table of at least 5 values, then plot those points on a coordinate plane.This activity will review the lesson from yesterday, and it will serve as an introduction tofunctions—today’s lesson. See page 12.Objective/Purpose (behavioral objectives, at the end of the lesson the students will)Primary (math related) Students will be able to determine whether or not a relation is afunction. Students will be able to write and interpret equations in function notation. Students willrecognize functions as relations between two quantities.Secondary (social, citizenry, teamwork, etc,) Students will have to share materials at thestations and take turns in some cases—this will teach them important social skills about beingpatient and sharing materials.Input / Prior Knowledge (What information is essential for the student to know before beginningand how will this skill be communicated to students?): Students will need to know basicinformation about the coordinate plane: which axis is the x-axis vs. the y-axis, how to plot points,which quadrants negative numbers belong to. This information will be reviewed in the warm up,then the teacher will use it to introduce the new topics in today’s lesson.Model & Introduction (rationale – class, small group, pairs, individual) (how will youdemonstrate the skill or competency? class, small group, pairs, individual): 20-25 MinutesThe teacher will go over the warm up and state that the equation y mx b is a linearequation because x is to the first power. The teacher will then point out that this equation isalso a function, which can be seen by the graph of a straight line. However, not all functionsare straight lines, as will be discussed later in the lesson.The teacher will go over last night’s homework by posting the answers and walking aroundthe room checking for completeness. If students have questions over particular problems,the teacher will answer those questions before moving on to new content.The teacher will distribute the resource page for this lesson to each student (see page 13).This page includes blanks for students to fill in definitions as well as pictures of graphs toserve as examples of functions vs. non-functions. The visuals appeal to visual learners andthe blanks will help keep students engaged in the lesson—they have to listen to learn thedefinitions. This also builds student independence because they have to write down thedefinitions or their resource page will not be as helpful.The teacher will review the vocabulary. She will post the definition of each word (function,domain, range, vertical line test, function notation) one at a time, and give examples andvisuals. These examples will come from pages 226-227 in the textbook. The teacher willgive examples of linear functions as well as non-linear functions.Teacher Hint: Make sure to give examples of non-linear functions so that students do notbuild the misconception that only straight lines are functions.The teacher will hand out the packet (see pages 15-18) that will accompany the stationsactivity today. The teacher will briefly describe the activity and remind students thatfunctions represent a relationship between two quantities. For example, if a car is driving at55mph, the distance that car travels is a function of the amount of time it is traveling.
11Developmental Activity (Teaching: cues, reinforcement, practice, feedback, involvement) (Listactivities which will be used to allow student practice): 20 minutesStudents will travel around the room going to different stations and filling out theirworksheet individually. When at each station, students may work with each other, but arestill responsible for filling out their own worksheet.At each station, there will be directions to demonstrate how one quantity relates to another.This activity will benefit kinesthetic and visual learners. It will help all students understandconceptually what a function is. The stations are as follows (all materials will be provided ateach station):o Measuring the length of consecutive pencils: length is a function of the number ofpencils—length increases with the number of pencils.o Putting rocks in a zip-lock bag attached to a rubber band: the more rocks added, themore the rubber band stretches—length of the rubber band is a function of weightadded to the bago Stack Jenga blocks in 5 seconds and 15 seconds. The number of blocks stacked is afunction of how much time you had.o Circle cut-outs and beads: the larger circles require more beads to cover them—areais a function of radius.This activity will require to make a hypothesis and will use the scientific vocabulary ofindependent variable and dependent variable. Each station can be looked at as a scientificexperiment. This interdisciplinary content will help students learn the material.Check for Understanding (Formative assessment: Identify strategies to be used to determine ifstudents have learned the objectives.): While students are working at the stations, the teacher willfloat around the classroom make observations and answering questions. In addition, the teacher canread responses from the station packets and exit slips to see who is understanding today’sobjectives. While walking around the classroom making observations, the teacher can ask thefollowing guiding questions to check for understanding: Which variable is the independent/dependent variable?How does the independent/dependent variable relate to the domain/range of the function?Why is this relation a function?Can you give me an example of a relation that is not a function?Closing Activity / Reflection – involves all students, to identify students’ success with the dailyobjective – rationale for choice, ex. Exit slip) Time: 5 minutes. Students will fill out an exit slip inorder to identify what they learned and what they are taking away from this lesson. The exit slipwill ask them questions pertaining to the main ideas of today’s lesson, which will allow the teacherto see who met the objectives. See page 19.Homework 4-15 page 229 in the textbookSummative Assessment Unit test on Day 11
12Warm UpDay 2Given the equation y 6x 8, complete the following table and plot the points on a coordinateplane.XY-10123Warm Up KeyDay 2XY-1208114220326
13Resource Notes PageDay 2Introduction to FunctionsA function is a in which each element of the is paired with exactly oneelement of the .The domain is the set of all of a function.The range is the set of all of a function.This is not a function because:This is a function because:For graphs, we can use the vertical line test. If a vertical line can be drawn so that it intersects thegraph , then the graph is not a function.Function notation is a way to write equations. Instead of y 3x, we write f(x) 3x. Therepresents elements in the domain and represents elements in the rangeIf you want to find the value in the range that corresponds to 4 in the domain, you writeand it is read “f of 4.” The value is found by substituting 4 in for x in the equation.Practice: If f(x) 2x 5, find each valuef(1)f(1/2)
14Resource Notes Page KeyDay 2Introduction to FunctionsA function is a relation in which each element of the domain is paired with exactly one element ofthe range.The domain is the set of all inputs of a function.The range is the set of all outputs of a function.This is not a function because:an input has more than one output.This is a function because:each input has exactly one output.For graphs, we can use the vertical line test. If a vertical line can be drawn so that it intersects thegraph more than once, then the graph is not a function.Function notation is a way to write equations. Instead of y 3x, we write f(x) 3x. The xrepresents elements in the domain and f(x) represents elements in the rangeIf you want to find the value in the range that corresponds to 4 in the domain, you write f(4) and itis read “f of 4.” The value is found by substituting 4 in for x in the equation.Practice: If f(x) 2x 5, find each valuef(1) 7f(1/2) 6
15Stations Worksheet (page 1)Day 2Station One—Pencil StationAt this station, we will be looking at the relationship between length covered and number of pencilslaid down. The independent variable, the one we have control over, is the number of pencils laiddown. The dependent variable, the one that changes due to the number of pencils, is the lengthcovered.1. Before you begin, as we increase the number of pencils laid down, what do you think willhappen to the length covered?a. Hypothesis:2. Measure and record the length of one pencil in centimeters using the ruler provided.a. Length of one pencil:3. Lay down another pencil at the end of your first pencil. Measure and record the new length:a. Length of 2 pencils:4. What will happen if we continue to lay down one more pencil to the end of the chain? Youmay try this several times with the extra pencils.a. As we add more pencils to the chain5. In this situation, our input values, or domain, are the number of pencils laid down. What arethe output values, or range?6. Think about if we were to graph this relation:a. Which variable would go on the x-axis?b. Which variable would go on the y-axis?7. Is this relation a function? (Hint: think about whether or not each element of the domain ispaired with exactly one element of the range.)
16Stations Worksheet (page 2)Day 2Station Two—Rocks StationAt this station, we will be looking at the relationship between length of the rubber band and thenumber of rocks placed in the zip-lock bag. The independent variable, the one we have controlover, is the number of rocks. The dependent variable, the one that changes due to the number ofrocks, is the length of the rubber band.1. Before you begin, as we increase the number of rocks in the bag, what do you think willhappen to the length of the rubber band?a. Hypothesis:2. Measure and record the length of the rubber band with an empty bag in centimeters usingthe ruler provided.a. Length of rubber band:3. Add 3 rocks to the bag. Measure and record the new length of the rubber band:a. Length of rubber band:4. What will happen if we continue to add more rocks to the bag? You may try this severaltimes with the extra rocks.a. As we add more rocks to the bag5. In this situation, our input values, or domain, are the number of rocks in the bag. What arethe output values, or range?6. Think about if we were to graph this relation:a. Which variable would go on the x-axis?b. Which variable would go on the y-axis?7. Is this relation a function? (Hint: think about whether or not each element of the domain ispaired with exactly one element of the range.)
17Stations Worksheet (page 3)Day 2Station Three—Jenga StationAt this station, we will be looking at the relationship between the amount of time and the number ofJenga blocks stacked. The independent variable, the one we have control over, is amount of time.The dependent variable, the one that changes due to the amount of time, is the number of blocksstacked.1. Before you begin, as we increase the amount of time you have to work, what do you thinkwill happen to the number of blocks you are able to stack?a. Hypothesis:2. Start the timer and stack blocks for 5 seconds. Record the number of blocks you stacked:a. Number of blocks stacked:3. Unstack your blocks, then start the timer and stack blocks for 15 seconds. Record thenumber of blocks you stacked:a. Number of blocks stacked:4. What will happen if we continue increase the amount of time you have to work? You maytry this several times. Make sure you always unstack your blocks from the previous trial.a. As we increase the amount of time5. In this situation, our input values, or domain, are the number of seconds you had to stack.What are the output values, or range?6. Think about if we were to graph this relation:a. Which variable would go on the x-axis?b. Which variable would go on the y-axis?7. Is this relation a function? (Hint: think about whether or not each element of the domain ispaired with exactly one element of the range.)
18Stations Worksheet (page 4)Day 2Station Four— Beads StationAt this station, we will be looking at the relationship between the size of the circle and the numberof beads necessary to cover the surface of the circle. The independent variable, the one we havecontrol over, is size of the circle. The dependent variable, the one that changes due to the size of thecircle, is the number of beads.1. Before you begin, as we increase the size of the circle, what do you think will happen to thenumber of beads you need to cover the surface of the circle?a. Hypothesis:2. Take the smallest circle and cover it completely with beads. Record the number of beadsyou used:a. Number of beads:3. Take the next smallest circle and cover it completely with beads. Record the number ofbeads you used:a. Number of beads:4. What will happen if we continue increase the size of the circle? You may try this severaltimes with the larger circles and extra beads.a. As we increase the size of the circle5. In this situation, our input values, or domain, are sizes of the circles. What are the outputvalues, or range?6. Think about if we were to graph this relation:a. Which variable would go on the x-axis?b. Which variable would go on the y-axis?7. Is this relation a function? (Hint: think about whether or not each element of the domain ispaired with exactly one element of the range.)
19Exit SlipDay 2What is a function?How can you determine whether or not a relation is a function?
20Linear FunctionsDay 3—Understanding SlopeEssential Question: W
3 Linear Functions Day 1—Graphing Linear Equations Essential Question: How do we graph linear equations and how can we use those graphs? Common Core/Objective: CCSS.Math.Content.8.F.A.3 Interpret the equation y mx b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.
Feeny Math Resources Linear Functions Linear Functions Linear Functions Linear Functions Linear Functions Which of the following is a solution to the linear function in the graph? A. (1,1) B. (5,3) C. (
mx b a linear function. Definition of Linear Function A linear function f is any function of the form y f(x) mx b where m and b are constants. Example 2 Linear Functions Which of the following functions are linear? a. y 0.5x 12 b. 5y 2x 10 c. y 1/x 2 d. y x2 Solution: a. This is a linear function. The slope is m 0.5 and .
Algebra 1 Unit 5: Comparing Linear, Quadratic, and Exponential Functions Notes 2 Standards MGSE9-12.F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions. MGSE9-12.F.LE.1a Show that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals.
Unit 1 - Transformations of Functions and Geometric Objects Unit 2 - Similarity and Congruency Unit 3 - Quadratic Functions Unit 4 - Square Roots and Inverse Variation Functions Unit 5 - Relationships in Triangles Unit 6 - Probability Unit 1 - Functions and their Inverses Unit 2 - Exponential and Logarithmic Functions Unit 3 - Polynomial .
SKF Linear Motion linear rail INA Linear SKF Linear Motion Star Linear Thomson Linear linear sysTems Bishop-Wisecarver INA Linear Pacific Bearing Thomson Linear mecHanical acTuaTors Duff-Norton Joyce/Dayton Nook Industries Precision mecHanical comPonenTs PIC Design Stock Drive Product
functions: linear functions and exponential functions. We will begin with linear functions, but first, we need to extend the idea of unit analysis one step further. Part 1 Applying Unit Analysis to Sums and Differences The underlying principle behind unit analysis can be illustrated by the following senseless statements: 6 horses 6 turtles
Section 8: Summary of Functions Section 8 – Topic 1 Comparing Linear, Quadratic, and Exponential Functions – Part 1 Complete the table below to describe the characteristics of linear functions. Linear Functions Equation ! # & Shape linear Rate of Change constant Number of ’-intercepts (or ) or infinitely many Number of *-intercepts )
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