Answer
$\text{(a)}$ domain $[-5,5]$; range $[-3,3]$.
$\text{(b)}$ $x$-intercepts: $-2$ and $2$; $y$-intercept: $2$
$\text{(c)}$ $f(1)=3$.
$\text{(d)}$ $x=-5$ and $x=3$
$\text{(e)}$ $x\in[-5,-2)\cup(2,5]$
Work Step by Step
(a) The $x$ values range from $-5$ to $5$ so the domain is $[-5,5]$. The $y$ values range from $-3$ to$3$ so the range is $[-3,3]$.
(b) The graph crosses the $x$-axis at $(-2,0)$ and $(2,0)$ so the $x$-intercepts are $-2$ and $2$.
The graph crosses the $y$-axis at $(0,2)$ so the $y$-intercept is $2$..
(c) The graph contains the point $(1, 3)$ so $f(1)=3$.
(d) Locate points where the $y$-value is $-3$. Since the graph contains $(-5, -3)$ and $((3, -3)$, then $f(-5)=-3$ and $f(3)=-3$. Thus, the solutions are $x=-5$ and $3$.
(e) The solution to $f(x) \lt 0$ are the $x$-values of the parts of the graph that are below the $x$-axis. Thus, the values of $x$ for which $f(x)<0$ are the ones in the intervals $[-5,-2)$ and $(2,5]$.
Therefore, the solution set is $[-5, -2)\cup (2, 5]$..
