Problem 2
Question
What is the domain of a relation?
Step-by-Step Solution
Verified Answer
The domain of a relation is the set of all input values (x-values) of the ordered pairs in the relation. For example, if we have the relation R = \(\{(1,2), (2,4), (3,6), (4,8)\}\), the domain of this relation would be Domain(R) = \(\{1, 2, 3, 4\}\).
1Step 1: 1. Defining Domain of a Relation
In mathematics, a relation is a set of ordered pairs, where each ordered pair consists of an input value and an output value (usually represented as \((x,y)\) or \((a,b)\)). The domain of a relation is the set of all input values (x-values). It is essential to understand the domain, as it represents all the possible values for a function or relation's input.
2Step 2: 2. Example of a Relation and Finding its Domain
Let's say we have a relation represented by the following set of ordered pairs:
R = \(\{(1,2), (2,4), (3,6), (4,8)\}\)
This relation consists of 4 ordered pairs, each with an input value and an output value. To find the domain, we simply list all the input values (x-values) without repetition:
Domain(R) = \(\{1, 2, 3, 4\}\)
In this case, the domain of relation R includes the values 1, 2, 3, and 4.
Other exercises in this chapter
Problem 2
If \(a\) varies inversely as \(b\), then as \(b\) increases, the value of \(a\)_________
View solution Problem 2
Given a quadratic function of the form \(f(x)=a(x-h)^{2}+k,\) answer the following. What is the equation of the axis of symmetry?
View solution Problem 3
For each pair of functions, find a) \((f+g)(x)\) b) \((f+g)(5), \text { c) }(f-g)(x), \text { and } \mathrm{d})(f-g)(2)\) $$f(x)=4 x^{2}-7 x-1, g(x)=x^{2}+3 x-6
View solution Problem 3
Graph each function by plotting points, and identify the domain and range. $$k(x)=\frac{1}{2}|x|$$
View solution