First, let's list the roots, we can see in the graph that it's
[tex]\begin{gathered} z_1=-1 \\ z_2=1 \\ z_3=-3 \\ z_4=3 \end{gathered}[/tex]We can see that the graph crosses the x-axis on all roots then they all have simple multiplicity (1). Then we know that the polynomial is something like
[tex]\begin{gathered} p(x)=a(x-z_1)(x-z_2)(x-z_3)(x-z_4) \\ \\ p(x)=a(x+1)(x-1)(x+3)(x-3) \end{gathered}[/tex]We can find the domain and the range graphically, we know that polynomial functions do not have any domain restriction, therefore
[tex]\text{ domain = }\mathbb{R}[/tex]For the range, we must see which values the polynomial can take, usually, even powered polynomials have a restricted range, here the degree is 4, then it must be restricted.
We can see in the graph that the function does not take any value under -16, therefore the range is
[tex]\text{ range = \textbraceleft y }\ge\text{ -16\textbraceright}[/tex]___________________________________
Now to find the equation, let's remember that
[tex]p(x)=a(x+1)(x-1)(x+3)(x-3)[/tex]We do not have the value of "a", but we know that when x = 0 we have y = 9, we can use that to find a
[tex]\begin{gathered} 9=a(0+1)(0-1)(0+3)(0-3) \\ \\ 9=a\cdot9 \\ \\ a=\frac{9}{9} \\ \\ a=1 \end{gathered}[/tex]Therefore the equation is
[tex]p(x)=(x+1)(x-1)(x+3)(x-3)[/tex]We can also do the distributive
[tex]\begin{gathered} p(x)=(x^2-1)(x^2-9) \\ \\ p(x)=x^4-10x^2+9 \end{gathered}[/tex]