College Algebra (10th Edition)

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

Chapter 3 - Section 3.1 - Functions - 3.1 Assess Your Understanding: 83

Answer

$\displaystyle 2x+h-1$

Work Step by Step

We are given: $f(x)=x^{2}-x+4$ We find the difference quotient: $\displaystyle \frac{f(x+h)-f(x)}{h}$ $\displaystyle =\frac{(x+h)^{2}-(x+h)+4-(x^{2}-x+4)}{h}$ $\displaystyle =\frac{x^{2}+2xh+h^{2}-x-h+4-x^{2}+x-4}{h}$ $\displaystyle =\frac{2xh+h^{2}-h}{h}$ $\displaystyle =\frac{h(2x+h-1)}{h}$ $\displaystyle =2x+h-1$
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