College Algebra (10th Edition)

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

Chapter 4 - Section 4.3 - Quadratic Functions and Their Properties - 4.3 Assess Your Understanding - Page 300: 64

Answer

(a) See below. (b) Domain: $(-\infty, \infty)$ Range:$[-8, \infty)$ (c) Domain where function decreases:$(-\infty, 1]$ Domain where function increases: $[1, \infty)$

Work Step by Step

First, we convert to vertex form to find the range and increasing and decreasing domains easier: $f(x)=x^2-2x-8$ $f(x)=x^2-2x+1-8-1$ $f(x)=(x-1)^2-9$ Recap: The domain is a horizontal span from the function's smallest value of x to the function's largest value of x. The range is a vertical span from the function's smallest value of f(x) to the function's largest value of f(x). A function is increasing in the domain intervals where its slope is positive. On the other hand, a function is decreasing in the domain intervals where its slope is negative. In a quadratic function, we can find where the function starts or stops increasing by locating the vertex.
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