# MA.912.A.2.4 Domain and Range of Relations

## Rationals-Discrete

Lesson 1-6 Pages 39-44 (Example 1)

## What You Need To Know...

Determine the domain and range of a relation.

1. The benchmark will be assessed using MC (Multiple Choice) and FR (Fill in Response) items.
2. Items may require students to determine the domain and/or range from an equation. Only linear and quadratic functions may be used.
3. Domains and ranges may be listed as inequalities or written as a sentence.
4. Items may present relations in a variety of formats, including sets of ordered pairs, tables, graphs, and input/output models.
5. Only linear, quadratic, or piecewise functions may be used.
6. Items may require students to identify the upper or lower bound of the relation.

## Example One

An economics teacher plotted the value of a stock on 11 different days during a 500-day period and used line segments to connect them.  In the graph below, the horizontal axis is measured in days and the vertical axis is measured in dollars.

Based on the graph, which of the following best describes the range of the value of stock for this 500 day period?

A.   0 < < 500
B.   1 < < 500
C. 10 < y < 60
D.   0 < y < 10

## Example Two

The set of ordered pairs shown below defines a relation.

{(0, 0), (1, 5), (2, 8), (3, 9), (4, 8), (5, 5), (6, 0)}

What is the value of the greatest element in the range of this relation?

## Example Three

J'Nai has a radio-controlled airplane that weighs 7 kilograms (kg).  The equation below shows k, the kinetic energy of a 7 kg object, as a function of v, its velocity in meters per second (m/s).

J'Nai found that her plane could do a certain trick if the plane was going at least 8 m/s but no more than 12 m/s.  What is the greatest value in the range?