Answer
(a) x-intercepts $x=-5,-1,5$, y-intercept $y=-3$.
(b) no symmetry.
(c) neither.
(d) increasing $(-\infty,-3),(2,\infty)$, decreasing $(-3,2)$.
(e) $x=-3$, $f(-3)=5$.
(f) $x=2$, $f(2)=-6$.
Work Step by Step
(a) Based on the given graph, we can determine the x-intercepts $x=-5,-1,5$, and y-intercept $y=-3$.
(b) Based on the graph, we can not identify any specified symmetry.
(c) Based on the graph, we can see it is neither even nor odd.
(d) We can find the intervals on which $f$ is increasing as $(-\infty,-3),(2,\infty)$ and the interval on which $f$ is decreasing as $(-3,2)$.
(e) A local maximum happens at $x=-3$ with $f(-3)=5$.
(f) A local minimum happens at $x=2$ with $f(2)=-6$.
