College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 2, Functions - Section 2.4 - Average Rate of Change of a Function - 2.4 Exercises: 25

Answer

(a) $\frac{1}{2}$ (b) the slope is also $\frac{1}{2}$

Work Step by Step

(a) We find the average rate of change from $x=a$ to $x=a+h$: $\displaystyle \frac{f(a+h)-f(a)}{(a+h)-a}=\frac{[\frac{1}{2}(a+h)+3]-[\frac{1}{2}a+3]}{h}=\frac{\frac{1}{2}a+\frac{1}{2}h+3-\frac{1}{2}a-3}{h}=\frac{\frac{1}{2}h}{h}=\frac{1}{2}$ (b) A line has the form $f(x)=mx+b$, with $m=slope$. For the line $f(x)=\displaystyle \frac{1}{2}x+3$, the slope is $\displaystyle \frac{1}{2}$, which equals what we got in (a).
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