Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 1 - Section 1.3 - Linear Functions and Models - Exercises - Page 90: 12

Answer

$g(x)$ is linear, $f(x)$ is not $g(x)=\displaystyle \frac{1}{2}x-4$

Work Step by Step

For linear functions, a change of $\Delta x$ units in results in a change of $\Delta y=m\Delta x$ units in $y$. The table shows changes in x of $\Delta x=+1$0, (constant throughout the row) so the linear function will have constant changes of y, $\Delta y$. f(x) has consecutive $\Delta y$ of $\ \ 1.5, 1.5, 1.0, 1.0$ ... not constant, so it is not linear g(x) has consecutive $\Delta y$ of 5,5,5,5 ... constant, therefore g is linear The equation of g is of the form $f(x)=mx+c$, (m=slope, b=y-intercept) From this table, for every change in x of $\Delta x=+10$, the change in y=f(x), $\Delta y=+5$, so $m=\displaystyle \frac{5}{10}=\frac{1}{2}. $ The table also gives $b=g(0)=-4$ (the y-intercept) So, $g(x)=mx+c$, $g(x)=\displaystyle \frac{1}{2}x-4$
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