lesson 5 problem solving practice compare properties of functions

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Lesson 5 Homework Practice Compare Properties Of Functions

Displaying top 8 worksheets found for - Lesson 5 Homework Practice Compare Properties Of Functions .

Some of the worksheets for this concept are Homework practice and problem solving practice workbook, , Lesson 4 homework practice, Homework practice and problem solving practice workbook, Lesson 39 comparison of functions, Word problem practice workbook, Lesson exponential functions, Holt algebra 1.

Found worksheet you are looking for? To download/print, click on pop-out icon or print icon to worksheet to print or download. Worksheet will open in a new window. You can & download or print using the browser document reader options.

1. Homework Practice and Problem-Solving Practice Workbook

2. connected.mcgraw-hill, 3. lesson 4 homework practice -, 4. homework practice and problem-solving practice workbook, 5. lesson 39: comparison of functions, 6. word problem practice workbook, 7. lesson 5.1 exponential functions, 8. holt algebra 1.

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Comparing Properties of Two Functions Worksheets

In math we use functions to model situations or phenomena that is consistent. While there may be some limits to the level of accuracy that be exhibited, they are very help for understanding a scenario and predicting changes that can be made to improve an outcome. There will be times when you have multiple options of how you can use a function and analyzing and comparing those possible uses of functions can indicate which would be best for our situation. We lean heavily on the use of graphs to understand the nature of functions, but they are not always practical solutions. In this section we will focus on analyzing function tables and algebraic comparisons. These worksheets and lessons teach students how to compare the various properties of functions.

Aligned Standard: Grade 8 Functions - 8.F.A.2

• Compare the Functions Step-by-Step Lesson - You are provided two functions in equation and table form. Compare them as best you can.
• Guided Lesson - We look at positive and negative slope and what it means about the relationship between the two functions.
• Guided Lesson Explanation - These problems involve a great deal of slope calculations. Make sure your students have that skill down pat before moving on to this skill.
• Independent Practice -Not only are the problems themselves lengthy, the answers take up a great deal of paper to solve.
• Matching Worksheet - Solve all the word problems to find their match. This one only has 4 problems because of the sheer volume the problems take up.
• Co Functions Worksheet Five Pack - This pack and the next is here to show you the next level of material that is coming up for this topic.
• Composition of Functions Worksheet Five Pack - This really boils down to the old plug the numbers in and solve type of problem.
• Answer Keys - These are for all the unlocked materials above.

Homework Sheets

Compare the functions and the input/output charts for slope.

• Homework 1 - The equation of straight line is y = mx +b Slope is the rate of change. The coefficient of x is the slope of the line.
• Homework 2 - Compare the two linear functions listed below and determine which has a negative slope.
• Homework 3 - Will is a shop keeper. He has 25 toys at the start of the day. He sold 5 toys per day. Write the rule for the total number of sold toys as a function of the number of days (d). c = 25 - 5d

Practice Worksheets

This is a skill that covers a lot of ground and can be interpreted many different ways.

• Practice 1 - Roy starts with $100. He spends $10 per week. Let y be the amount remaining as a function of the number of weeks, x.
• Practice 2 - Determine which has the greater rate of change.
• Practice 3 - Compare the following functions to determine which has the greater rate of change.

Math Skill Quizzes

The variable g(x) is introduced and sometimes it will make the kids' heads' spin

• Quiz 1 - Compare the following functions to determine which has the greater rate of change.
• Quiz 2 - Using f(x) = 5x + 5 and g(x) = x + 2, find: f[f(3)]
• Quiz 3 - Simplify Cot (90-x) tan x

How to Compare the Properties of Two Functions

A function is a mathematical relationship that takes in an input and based on the rule that is assigned will produce an output. They are a concept which needs to be adequately understood so that it doesn't create problems in the future. Most students might not know that this concept will get more difficult as you move to higher classes. Functions can be represented in many different ways. The most common ways to illustrate them is through the use of an input-output table, equation, or graph. There are three ways to compare the math relationships, i.e., algebraically, numerically, and graphically.

Let us compare two functions numerically. Let us consider an example of y = 3x + 5. In this example, y is a dependent of x, so in other words, if we keep on changing the value of x, then y will increase as well. Let's look at the table as an example.

x, y = (-1, 2), (0, 5), (4, 17), (-5, -10)

Comparing functions graphically is probably the easiest to understand. You cannot always use this method because sometimes the inputs and outputs simply do not fit neatly on a coordinate plane. We compared the graph of two functions below:

Can you spot any significant trends? Starting with the function represented by the blue line, we can clearly see that as the value of x increases, the value of y decreases. The function represented by the green line, on the other hand, has a much different trend. As the value of x increases, on the green line, so does the value of y. Graphs like this help us understand the nature of functions and make solid predictions of them.

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Lesson 5 Homework Practice Compare Properties Of Functions

Lesson 5 Homework Practice Compare Properties Of Functions - Displaying top 8 worksheets found for this concept.

Some of the worksheets for this concept are Homework practice and problem solving practice workbook, , Lesson 4 homework practice, Homework practice and problem solving practice workbook, Lesson 39 comparison of functions, Word problem practice workbook, Lesson exponential functions, Holt algebra 1.

Found worksheet you are looking for? To download/print, click on pop-out icon or print icon to worksheet to print or download. Worksheet will open in a new window. You can & download or print using the browser document reader options.

1. Homework Practice and Problem-Solving Practice Workbook

2. connected.mcgraw-hill, 3. lesson 4 homework practice -, 4. homework practice and problem-solving practice workbook, 5. lesson 39: comparison of functions, 6. word problem practice workbook, 7. lesson 5.1 exponential functions, 8. holt algebra 1.

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Common Core: 8th Grade Math : Compare Properties of Two Functions: CCSS.Math.Content.8.F.A.2

Study concepts, example questions & explanations for common core: 8th grade math, all common core: 8th grade math resources, example questions, example question #1 : compare properties of two functions: ccss.math.content.8.f.a.2.

The table and the equation provided represent two different functions. Which of these two functions—either table or equation form—has the greater rate of change, and what is the rate of change? 

The rate of change is also known as the slope. As we have learned we can use the following equation to solve for the slope of the table:

An input/output table displays sets of ordered pairs. The input column represents the x-values and the output column represents the y-values. We can select two sets of ordered pairs from the table to solve for the slope:

In order to determine the slope of the equation, we need to make sure the equation is in slope-intercept form: 

Example Question #2 : Compare Properties Of Two Functions: Ccss.Math.Content.8.F.A.2

Example Question #3 : Compare Properties Of Two Functions: Ccss.Math.Content.8.F.A.2

Example Question #4 : Compare Properties Of Two Functions: Ccss.Math.Content.8.F.A.2

Example Question #5 : Compare Properties Of Two Functions: Ccss.Math.Content.8.F.A.2

Example Question #7 : Compare Properties Of Two Functions: Ccss.Math.Content.8.F.A.2

Example Question #8 : Compare Properties Of Two Functions: Ccss.Math.Content.8.F.A.2

Example Question #9 : Compare Properties Of Two Functions: Ccss.Math.Content.8.F.A.2

Example Question #10 : Compare Properties Of Two Functions: Ccss.Math.Content.8.F.A.2

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Curriculum  /  Math  /  8th Grade  /  Unit 4: Functions  /  Lesson 10

Lesson 10 of 12

Criteria for Success

Tips for teachers, anchor problems, problem set, target task, additional practice.

Compare functions represented in different ways (Part 2).

Common Core Standards

Core standards.

The core standards covered in this lesson

8.F.A.2 — Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

Foundational Standards

The foundational standards covered in this lesson

Ratios and Proportional Relationships

7.RP.A.2.B — Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

7.RP.A.2.C — Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

7.RP.A.2.D — Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

The essential concepts students need to demonstrate or understand to achieve the lesson objective

• Interpret and compare functions in context of the situation described.
• Identify rate of change in graphs, tables, equations, and verbal descriptions and compare across representations.
• Identify initial value in graphs, tables, equations, and verbal descriptions and compare across representations.

Suggestions for teachers to help them teach this lesson

• This lesson includes one Anchor Problem, which is longer than a typical Anchor Problem. You may want to allow students to work in pairs or small groups after some independent time with the problem. 
• Lesson 10, a continuation from Lesson 9, brings together the concepts and skills from the previous lessons in the unit in order to interpret and compare functions presented in different formats. 

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

Sam wants to take his music player and his video game player on a car trip. An hour before they plan to leave, he realized that he forgot to charge the batteries last night. At that point, he plugged in both devices so they can charge as long as possible before they leave.

Sam knows that his music player has 40% of its battery life left and that the battery charges by an additional 12 percentage points every 15 minutes.

His video game player is new, so Sam doesn’t know how fast it is charging but he recorded the battery charge for the first 30 minutes after he plugged it in.

a.   If Sam’s family leaves as planned, what percent of the battery will be charged for each of the two devices when they leave?

b.   How much time would Sam need to charge the battery 100% on both devices?

Guiding Questions

Battery Charging , accessed on Oct. 31, 2017, 4:05 p.m., is licensed by Illustrative Mathematics under either the  CC BY 4.0  or  CC BY-NC-SA 4.0 . For further information, contact Illustrative Mathematics .

A set of suggested resources or problem types that teachers can turn into a problem set

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Function A is shown in the table below.

Four more functions are represented below. Find:

• a function that is the same as Function A
• a function with the same rate of change as Function A but with a different initial value
• a function with the same initial value as Function A but with a different rate of change
• a function with a greater rate of change than Function A

Student Response

An example response to the Target Task at the level of detail expected of the students.

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

• Have students represent functions in four ways (tables, equations, graphs, verbal descriptions). If students use notecards to represent the functions, then they can use the notecards in various ways. For example, students could form groups and play Memory with the note cards, turning them over and finding matching pairs. Or, students could make comparisons between the notecards based on rate of change or initial value. The goal of these activities is to enable students to see functions in various representations and to compare across those representations. 
• EngageNY Mathematics Grade 8 Mathematics > Module 5 > Topic A > Lesson 7 — Exercises 1 – 4, Problem Set; use remaining problems not used in Lesson 9; do not include parts of questions where students solve using systems of equations as they have not gotten to that unit yet

Topic A: Defining Functions

Define and identify functions.

Use function language to describe functions. Identify function rules.

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Topic B: Representing and Interpreting Functions

Identify properties of functions represented in tables, equations, and verbal descriptions. Evaluate functions.

8.F.A.1 8.F.A.2 8.F.B.4

Represent functions with equations.

8.F.A.1 8.F.B.4

Read inputs and outputs in graphs of functions. Determine if graphs are functions.

Identify properties of functions represented in graphs.

Topic C: Comparing Functions

Define and graph linear and nonlinear functions.

Determine if functions are linear or nonlinear when represented as tables, graphs, and equations.

8.F.A.1 8.F.A.3

Compare functions represented in different ways (Part 1).

Topic D: Describing and Drawing Graphs of Functions

Describe functions by analyzing graphs. Identify intervals of increasing, decreasing, linear, or nonlinear activity.

Sketch graphs of functions given qualitative descriptions of the relationship.

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• 7th 8th grade math comparing linear functions

7th & 8th Grade Math - Comparing Linear Functions

In fall of 2008, Sally Keyes (math coach), Kamaljit Sangha (7/8 math teacher/department leader) and Cecilio Dimas (7/8 math teacher) developed our first lesson on cost-analysis. By the end of fall 2008, all eleven 7th grade classes, regular and accelerated, had been taught the DVD Plan lesson. The foundation of this lesson is constructing, communicating, and evaluating student-generated tables while making comparisons between three different financial plans. Students had been given three different DVD rental plans and asked to analyze each one to see if they could determine when the 3 different DVD plans cost the same amount of money, if ever. Using this idea as an anchor problem taken from our original pre-assessment with the MARS task "Gym," we were devising avenues for our students to explore and understand specific multiple representations of breaking points. We believe that being able to understand multiple representations for the breaking even points in a written explanation, a table, a graph, and an algebraic rule is critical to success in algebra. The design of our year-long lesson study is to address each of these multiple representations: verbal, tabular, graphical, and algebraic generalization. Our perception is that students tend to see the graph as the “last thing” with no real connection to the mathematics of the situation or to other representations and that was our reason to put it after the verbal and tabular representations. Lesson Goals -Comparisons of different deals: do these representations make mathematical sense and do they match the mathematics of the three plans? -Verbal descriptions -Tables graphs -Algebraic rules

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