College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 2 - Functions and Graphs - Exercise Set 2.2: 62

Answer

The difference quotient for the given function is $2x+h-5$

Work Step by Step

$f(x)=x^{2}-5x+8$ Find the difference quotient $\dfrac{f(x+h)-f(x)}{h}$ Start by finding $f(x+h)$. Substitute $x$ by $x+h$ in $f(x)$ and simplify: $f(x+h)=(x+h)^{2}-5(x+h)+8=...$ $...=x^{2}+2xh+h^{2}-5x-5h+8$ Substitute the known values into the formula for the difference quotient: $\dfrac{f(x+h)-f(x)}{h}=...$ $...=\dfrac{x^{2}+2xh+h^{2}-5x-5h+8-(x^{2}-5x+8)}{h}=...$ $...=\dfrac{x^{2}+2xh+h^{2}-5x-5h+8-x^{2}+5x-8}{h}=...$ $...=\dfrac{2xh+h^{2}-5h}{h}=...$ Take out common factor $h$ from the numerator and simplify: $...=\dfrac{h(2x+h-5)}{h}=2x+h-5$ The difference quotient for the given function is $2x+h-5$
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