Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 1 - Review - Concept Check: 1

Answer

(a) A function is a map from one set $X$ to another $Y$ such that every element of the set $X$ maps to exactly one element of set $Y$. (b) The graph of the function $f$ is the set of points in the $xy$ plane that have $x$ as their first and $f(x)$ as their second coordinate: $(x,f(x))$. (c) If every vertical line intersects the curve only once then that curve is the graph of a function.

Work Step by Step

(a) A function is a map from one set $X$ to another $Y$ such that every element of the set $X$ maps to exactly one element of set $Y$. There can be no multiple elements of $Y$ corresponding to the same element of $x$. However, multiple elements of $X$ may be mapped to the same element of $Y$. (b) The graph of the function $f$ is the set of points in the $xy$ plane that have $x$ as their first and $f(x)$ as their second coordinate: $(x,f(x))$. (c) If every vertical line intersects the curve only once then that curve is the graph of a function. The vertical line represents the constant value of $x$. This condition means that to each $x$ corresponds unique value $f(x)$ which is required by the definition of the function.
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