# Functions

## Objective

Compare functions represented in different ways (Part 1).

## Common Core Standards

### Core Standards

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• 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.

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• 7.RP.A.2.B

• 7.RP.A.2.C

• 7.RP.A.2.D

## Criteria for Success

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

## Tips for Teachers

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• Lessons 9 and 10 bring together the concepts and skills from the previous lessons in the unit in order to interpret and compare functions presented in different formats. The EngageNY problems referenced in the Problem Set Guidance include several examples; spread these problems out across Lesson 9 and Lesson 10.
• Students continue to re-contextualize information they gather from tables and graphs in order to make comparisons and conclusions (MP.2).

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

## Anchor Problems

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### Problem 1

Mari and Lewis both have cell phone plans that give them each 10 gigabytes (GB) of data each month. The graph and table below show the remaining amount of data that Mari and Lewis have after each week in the month.

 Lewis's Phone Data Usage Week Number 0 1 2 3 4 Data Remaining (GB) 10 9.6 7.4 4.9 1.6
1. Who used more data after 2 weeks?
2. Between weeks 2 and 3, who used more data?
3. Who had more data remaining after 3 weeks? By how much?

### Problem 2

At the Atkinson Farm, you can pick your own vegetables. You pay a small fee to enter the farm, and then you pay a price per pound of vegetables you pick. The graph below shows the total cost as a function of pounds of vegetables.

The Jackson Farm also allows you to pick your own vegetables. You pay an entry fee of $15 and then$2.50 per each pound of vegetables you pick.

1. Which farm charges the higher entry fee?
2. Which farm charges more per pound of vegetables?
3. If you plan on buying 4 pounds of vegetables, which farm has the better deal?
4. If you plan on buying 10 pounds of vegetables, which farm has the better deal?

### Problem 3

Two functions are shown below.

Function 1:  ${y={2\over3}x +1}$

Function 2:

 $x$ $y$ 4 3 6 4.5 8 6 10 7.5

Ella states that Function 2 has a greater initial value because $3>1$. Tommy states that Function 2 has a greater rate of change because $1\frac{1}{2} > \frac{2}{3}$.

Do you agree with either Ella or Tommy? Explain your reasoning.

## Problem Set

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

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Cora and Daniel are both saving money each month. The total amount in their savings accounts is a function of the number of months they have been saving. Each account is represented below.

Cora: ${y=65x+100}$, where $y$ represents the total amount and $x$ represents number of months

Daniel:

1. Who started with more money in their savings account?
2. Who is saving at a faster rate? By how much?
3. After 6 months, who will have more money in their savings account?

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