Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.2 - Basics of Functions and Their Graphs - Exercise Set - Page 180: 114


If a vertical line parallel to the y-axis is drawn at any point on the graph and cuts the graph not more than once, then the graph represents a function.

Work Step by Step

Let R be a relation from set ${{S}_{1}}$ to set ${{S}_{2}}$ with ordered pair $\left( x,y \right)$. A relation can be of four types: (a) One–one relation: For one x, there is only one y. (b) Many–one relation: For many x, there is one y. (c) One–many relation: For one x, there are many y. (d) Many–many relation: For many x, there are many y. For the ordered pair $\left( x,y \right)$ in the relation R, if by putting one value of x only one value of y is obtained, then the relation is said to be a function. More than one value of x can give the same value of y without violating the definition of a function. Hence, a one–one relation and a many–one relation are functions. An example of a relation that is also a function is $y=x$ An example of a relation that is not a function is $\begin{align} & {{y}^{2}}=x \\ & y=\pm \sqrt{x} \end{align}$ The graph represented by ${{y}^{2}}=x$ is as follows:
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