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In the two parts (bullet points) of the definition of function in 1.3, the second one is the part you know from Precalculus. I am looking for you to think about the implications of the first one. How does this differ from a relation? Do not just quote what it says. I'm looking for you to understand this implication since it's not explicitly stated all the time in Precalculus like the second one is.

In the two parts (bullet points) of the definition of function in 1.3, the second one is the part you know from Precalculus. I am looking for you to think about the implications of the first one. How does this differ from a relation? Do not just quote what it says. I'm looking for you to understand this implication since it's not explicitly stated all the time in Precalculus like the second one is.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter1: Expressions And Functions
Section1.7: Functions
Problem 60PFA
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Please help me with number 2 I’m so confused.
1. What is the difference between the range of a relation and the co-domain of a relation? 2. In the two parts (bullet points) of the definition of function in 1.3, the second one is the part you know from Precalculus. I am looking for you to think about the implications of the first one. How does this differ from a relation? Do not just quote what it says. I'm looking for you to understand this implication since it's not explicitly stated all the time in Precalculus like the second one is.
Transcribed Image Text:1. What is the difference between the range of a relation and the co-domain of a relation? 2. In the two parts (bullet points) of the definition of function in 1.3, the second one is the part you know from Precalculus. I am looking for you to think about the implications of the first one. How does this differ from a relation? Do not just quote what it says. I'm looking for you to understand this implication since it's not explicitly stated all the time in Precalculus like the second one is.
Functions In Section 1.2 we showed that ordered pairs can be defined in terms of sets and we defined Cartesian products in terms of ordered pairs. In this section we introduced relations as subsets of Cartesian products. Thus we can now define functions in a way that depends only on the concept of set. Although this definition is not obviously related to the way we usually work with functions in mathematics, it is satisfying from a theoretical point of view, and computer scientists like it because it is particularly well suited for operating with functions on a computer. Definition A function F from a set A to a set B is a relation with domain A and co-domain B that satisfies the following two properties: 1. For every element x in A, there is an element y in B such that (x, y) E F. 2. For all elements x in A and y and z in B, if (x, y) EFand (x, z) E F, then y = z.
Transcribed Image Text:Functions In Section 1.2 we showed that ordered pairs can be defined in terms of sets and we defined Cartesian products in terms of ordered pairs. In this section we introduced relations as subsets of Cartesian products. Thus we can now define functions in a way that depends only on the concept of set. Although this definition is not obviously related to the way we usually work with functions in mathematics, it is satisfying from a theoretical point of view, and computer scientists like it because it is particularly well suited for operating with functions on a computer. Definition A function F from a set A to a set B is a relation with domain A and co-domain B that satisfies the following two properties: 1. For every element x in A, there is an element y in B such that (x, y) E F. 2. For all elements x in A and y and z in B, if (x, y) EFand (x, z) E F, then y = z.
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