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

$\mathrm{Decreasing:}\:\:\:(-\infty,0)$ $\mathrm{Increasing:}\:\:\:(0,\infty)$ Graph is symmetric with respect to the $\ \mathrm{y-axis}.$ $\mathrm{First\:Part:}\:\:$ 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).\$ We can write the given function $\ y=(-x)^{\frac{2}{3}}\$ as $\ y=\sqrt {(-x)^2}=\sqrt {x^2}.$ 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 is symmetric with respect to the $\ \mathrm{y-axis}.$ $\mathrm{Third\:Part:}\:\:$ The graph of the given function $\ y=\sqrt {x^2}\$ is decreasing on $\ (-\infty,0)\$ and is increasing on $\ (0,\infty).$