Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.2 Mathematical Models: A Catalog of Essential Functions - 1.2 Exercises - Page 33: 8

Answer

All the members of the family of linear functions $f(x)= 1 + m(x+3)$ have the point $(-3,1)$ in common.
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Work Step by Step

This commonality can be seen by graphing several members of the family and seeing that they intersect at $(-3,1)$. Alternatively, two arbitrary values of $m$ could be chosen, such as $m=1$ and $m=0$, and two functions with those values can be equated together as follows: $1 + 1(x+3) = 1+0(x+3)$ $1 + x + 3 = 1$ $x + 3 = 0$ $x = -3$ Which would result in $y=1$ when inputted into any member of the family of linear functions $f(x)= 1 + m(x+3)$. This may be harder to identify than simply graphing the functions, however.
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