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

Decreasing: $(0,\infty)$ Increasing: nowhere Graph has no symmetry.
$\mathrm{First\:Part:}\:\:$ 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{3}{2}}\$ as $\ y=-\sqrt{x^3}.$ The domain 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=-\sqrt{x^3}\$ is decreasing on $\ (0,\infty).$