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: 69

Answer

$a.\quad 5$ $b.\quad y=5x-2$

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. $m_{sec}=\displaystyle \frac{f(b)-f(a)}{b-a}$ --- $a.$ $f(3)=13, \quad f(1)=3$ Average rate of change of $f$ from 1 to $3:$ $\displaystyle \frac{f(3)-f(1)}{3-1}=\frac{13-3}{3-1}=\frac{10}{2}=5$ $b.$ We have slope $m=5$ and a point $(1,3)$. Point-slope equation of the secant: $y-y_{1}=m(x-x_{1})$ $y-3=5(x-1)$ $y=5x-5+3$ $y=5x-2$
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