Answer
(a) $(-5,0),(-1,0),(5,0),(0,-3)$.
(b) no symmetry
(c) neither even nor odd.
(d) increasing on $(-\infty,-3),(2,\infty)$, decreasing on $(-3,2)$.
(e) $x=-3$ with $f(-3)=5$.
(f) $x=2$ with $f(2)=-6$.
Work Step by Step
(a) From the given graph, we can determine the intercepts $(-5,0),(-1,0),(5,0),(0,-3)$.
(b) We can see that the graph is not symmetric with respect to the x-axis, the y-axis, or the origin.
(c) We can see that the function is neither even nor odd.
(d) The function is increasing on $(-\infty,-3),(2,\infty)$, decreasing on $(-3,2)$.
(e) We can find a local maximum at $x=-3$ with $f(-3)=5$.
(f) We can find a local minimum at $x=2$ with $f(2)=-6$.
