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 33: 7

Answer

(a) $y=2x+b$ (b) $y=mx+1-2m$ (b) $y=2x-3$

Work Step by Step

(a) In general, we have a specific form of a linear function, that is: $y=mx+b$ (where $m$ stands for the slope and b stands for the $y$-intercept). If $m=2$, the line function will get the following form: $y=2x+b$. Now we can graph several members of this family, for any arbitrary $b$ (Graph (a)). (b) In this case, we have to use another form of a linear function which formulates like this: $y-y_{1} = m(x-x_{1})$. Inputting the point $f(2)=1$, we will get: $y-1=m(x-2)$ $y=m(x-2)+1$ And then sketch a graph for any arbitrary $m$. (Graph (b)) (c) To find a function that belongs to both of these functions, we can input the characteristic value of (a) $m=2$ into function (b): $y=2(x-2)+1$ $y=2x-3$
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