Calculus: Early Transcendentals 8th Edition

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

Chapter 1 - Section 1.2 - Mathematical Models: A Catalog of Essential Functions. - 1.2 Exercises - Page 34: 9

Answer

All of the functions from the family are parallel to each other with the slope of $-1$. On the figure are the members of this family for $c=-2$(blue), $c=0$(orange) and $c=1$(green)

Work Step by Step

The general equation of linear function is $$f(x)=kx+c$$ where $k$ is the slope. Any given function from this family can be rewritten as $$f(x)=-x+c$$ We see that all of these functions are parallel to each other with the slope of $-1$. On the figure are the members of this family for $c=-2$(blue), $c=0$(orange) and $c=1$(green)
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