## University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson

# Chapter 1 - Section 1.1 - Functions and Their Graphs - Exercises - Page 12: 44

#### Answer

Decreasing: $(0,\infty)$ Increasing: nowhere Graph has no symmetry. #### Work Step by Step

$\mathrm{First\:Part:}\:\:$ According to the definitions: A function $\ f\$ defined on an interval is increasing on $\ (a, b)\$ if for every $\ x_1, x_2\$ $\in$ $(a, b)$ $\ x_1\le x_2\$ implies that $\ f(x_1)\le f(x_2).\$ A function $\ f\$ defined on an interval is decreasing on $\ (a, b)\$ if for every $\ x_1, x_2\$ $\in$ $(a, b)$ $\ x_1\le x_2\$ implies that $\ f(x_1)\ge f(x_2).\$ The domain of the given function $\ y=-4\sqrt{x}\$ is $\ [0,\infty).$ First of all, create a table with a few points to sketch the graph. $\quad \mathrm{See\:the\:table\:and\:graph\:above.}$ $\mathrm{Second\:Part:}\:\:$ Graph has no symmetry. $\mathrm{Third\:Part:}\:\:$ The graph of the given function $\ y=-4\sqrt{x}\$ is decreasing on $\ (0,\infty).$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.