College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 3 - Section 3.3 - Properties of Function - 3.3 Assess Your Understanding - Page 234: 70


$a.\quad-4$ $b.\quad y=-4x+1$

Work Step by Step

Average rate of change from $a$ to $b$ $=\displaystyle \frac{\Delta y}{\Delta x}=\frac{f(b)-f(a)}{b-a},\quad a\neq b$ The average rate of change of a function from $a$ to $b$ equals the slope of the secant line containing the two points $(a,f(a))$ and $(b,f(b))$ on its graph. $m_{sec}=\displaystyle \frac{f(b)-f(a)}{b-a}$ ---- $a.$ $f(5)=-19, \quad f(2)=-7$ Average rate of change of $f$ from 2 to 5: $\displaystyle \frac{f(5)-f(2)}{5-2}=\frac{-19-(-7)}{3}=-\frac{12}{3}=-4$ $b.$ We have slope $m=-4$ and a point $(2,-7)$. Point-slope equation of the secant: $y-y_{1}=m(x-x_{1})$ $y-(-7)=-4(x-2)$ $y=-4x+8-7$ $y=-4x+1$
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