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Chapter 2: Problem 109

What is a relation? Describe what is meant by its domain and its range.

Short Answer

Expert verified
A relation is a set of ordered pairs, where every first element belongs to the domain and every second element belongs to the range. The domain is the set of all possible first elements (inputs, or x-values), while the range is the set of all possible second elements (outputs, or y-values).

Step by step solution

01

Defining a Relation

A relation in mathematics is a set of ordered pairs (x, y), which describes a relationship between two elements, where x belongs to the first set (called the domain), and y belongs to the second set (called the range). In simpler terms, it's anything that links one set of values with another set of values.
02

Defining the Domain of a Relation

The domain of a relation is the set of all possible values that the first element (x) of the ordered pairs can take. It consists of all inputs, or x-values, which will 'produce' some output in the relation.
03

Defining the Range of a Relation

The range of a relation is the set of all possible values that the second element (y) of the ordered pairs can take. It refers to the output, or y-values, which can be 'produced' given the specific domain.

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Most popular questions from this chapter

determine whether each statement makes sense or does not make sense, and explain your reasoning. Find the area of the donut-shaped region bounded by the graphs of \((x-2)^{2}+(y+3)^{2}=25 \quad\) and \((x-2)^{2}+(y+3)^{2}=36\)

give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. $$ (x+1)^{2}+(y-4)^{2}=25 $$

write the standard form of the equation of the circle with the given center and radius. $$ \text { Center }(-4,0), r=10 $$

give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. $$ (x+2)^{2}+(y+2)^{2}=4 $$

write the standard form of the equation of the circle with the given center and radius. $$ \text { Center }(-3,5), r=3 $$
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