Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 1 - Linear Functions - 1.7 Functions and Function Notation - 1.7 Exercises - Page 106: 1

Answer

$a$ is the input which is the age in years; $G(a)$ is the output which is the Grade level; the relation is not a function

Work Step by Step

In the given, the input variable is the age, $a$, of the student in years, and the output is the grade level, $G(a)$. Some ordered pairs, $(a,G(a))$, that represent this situation are $(7, \text{Grade }1)$ and $(7, \text{Grade }2)$. This means that a $7$-year-old student may be in Grade $1$ or in Grade $2$. In the example of ordered pairs above, the first coordinate was repeated. Since the ordered pairs in functions should not have first coordinates that repeat, then the given situation does not describe a function.
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