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: 9

Answer

$f(x)=-x-5$

Work Step by Step

The function is linear, we are told, so $y=f(x)=mx+b$ (m=slope, b=y-intercept) For linear functions, a change of $\Delta x$ units in results in a change of $\Delta y=m\Delta x$ units in $y$ From this table, for every change in x of $\Delta x=-1$, the change in y=f(x), $\Delta y=+1$, so $m=\displaystyle \frac{1}{-1}=-1. $ From "Computing the y-Intercept of a Line": the y-intercept of the line passing through $(x_{1},y_{1})$ with slope $m$ is $b=y_{1}-mx_{1}$ which gives us, inserting $(x_{1},y_{1})=(-4,-1)$ $b=-1-(-1)(-4)=-5$ Therefore, $f(x)=mx+b$ $f(x)=-x-5$
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