# Functions

## Objective

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

## Common Core Standards

### Core Standards

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• 8.F.A.1 — Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. Function notation is not required in Grade 8.

• 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.

• 8.F.B.4 — Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

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• 6.EE.A.2.C

• 6.RP.A.2

• 7.RP.A.2.B

## Criteria for Success

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1. Find the rate of change of a function represented in a table, equation, and verbal description.
2. Find the initial value of a function represented in a table, equation, and verbal description.
3. Evaluate a function formula for given values.

## Tips for Teachers

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Lessons 3 and 4 focus on functions represented in tables, equations, and verbal descriptions. In Lesson 3, students analyze these representations to make sense of the relationships between the quantities (MP.2). They use their understanding of unit rate and constant of proportionality to determine the rate of change between quantities. They consider what a starting or initial value means in context of a situation, and how to determine these values from a table or equation.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

## Anchor Problems

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### Problem 1

The function formula below shows the relationship between temperature in degrees Fahrenheit and degrees Celsius. °F is a function of °C.

${F=\frac{9}{5}C+32}$

1. Determine what 28°C is in °F.
2. Determine what 23°F is in °C.

### Problem 2

Determine the rate of change in each situation. Then describe the relationship using function language (for example, ____ is a function of ____ because _____.)

1.
 Amount of watermelon in pounds, x 0 0.25 0.5 1.5 2 3 5 Cost of watermelon y $0$0.35 $0.70$2.10 $2.80$4.20 $7.00 1. ${d=25t}$, where $d$ is distance in miles and $t$ is time in hours 2. Giovanni can decorate $2$ cakes, $c$, every $5$ hours, $h$. #### Guiding Questions Create a free account or sign in to access the Guiding Questions for this Anchor Problem. ### Problem 3 Determine the starting or initial output value in each situation. 1.  Miles traveled in cab, x 0 1 3 4 Cost of cab ride, y$2.50 $4.75$9.25 $11.50 1.  Miles traveled in cab, x 1 2 4 5 Cost of cab ride, y$4.50 $7.00$12.00 \$14.50
1.    ${P=16d+20}$ where $P$ is the total number of pages read in a book and $d$ is the number of days

## 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.

• Include additional items similar to Anchor Problems #2 and #3, where students are given functions (as tables, as equations, as verbal representations) and are asked to find the rate of change and initial value.
• Include problems where students evaluate function formulas, such as
• Circumference/perimeter
• Area/volume
• Distance

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### Problem 1

The formula below represents simple interest, $I$, as a function of the principle amount, $P$, the simple interest rate, $R$, and the time of the investment, $T$.

$I=PRT$

Determine the principle amount, $P$, when ${8.50}$ of interest has been earned after ${1.25}$ years with an annual rate of $2$%.

### Problem 2

The table below shows the number of miles Alan biked over time. Alan biked at a constant speed. Find the rate of change.

 Time in hours, x 0 0.5 2 4 4.5 6 Miles biked, y 0 7.5 30 60 67.5 90

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