Answer
(a) See graph.
(b) $(-\infty,\infty)$, $[-4,\infty)$.
(c) increasing $(-1,\infty)$, decreasing $(-\infty,-1)$.
Work Step by Step
(a) Given $f(x)=x^2+2x-3=(x+1)^2-4$, we have $a=1\gt0$, thus the graph opens up with vertex $(-1,-4)$, axis of symmetry $x=-1$, y-intercept $f(0)=-3$ and x-intercept(s) $x=-1\pm2=-3,1$. See graph.
(b) Based on the graph, we can identify the domain as $(-\infty,\infty)$ and range as $[-4,\infty)$.
(c) Based on the graph, we can find that $f$ is increasing on $(-1,\infty)$ and decreasing on $(-\infty,-1)$.
