Answer
(a) $0$.
(b) $(-\frac{\pi}{2},\frac{\pi}{2})$
(c) $1$
(d) $x=0,\pi,2\pi$
(e) $x=-\frac{3\pi}{2},\frac{\pi}{2}$, $x=-\frac{\pi}{2},\frac{3\pi}{2}$.
(f) $x=-\frac{5\pi}{6},-\frac{\pi}{6},\frac{7\pi}{6},\frac{11\pi}{6}$.
(g) $x=k\pi$
Work Step by Step
Given $f(x)=sin(x)$, we have:
(a) y-intercept $f(0)=0$, see graph.
(b) increasing over $(-\frac{\pi}{2},\frac{\pi}{2})$
(c) absolution maximum $1$
(d) $f(x)=0$ at $x=0,\pi,2\pi$
(e) $f(x)=1$ at $x=-\frac{3\pi}{2},\frac{\pi}{2}$. $f(x)=-1$ at $x=-\frac{\pi}{2},\frac{3\pi}{2}$.
(f) $f(x)=-1/2$ at $x=-\frac{5\pi}{6},-\frac{\pi}{6},\frac{7\pi}{6},\frac{11\pi}{6}$.
(g) x-intercept(s) at $x=k\pi$ where $k$ is an integer.
