[tex]f(x) - \frac{x^{2}-4 }{x^{4} +x^{3} -4x^{2}-4 }[/tex]What is the:Domain:V.A:RootsLY-Int:H.A:Holes:O.A:Also, graph it.

a) The given function is[tex]f(x)=\frac{x^2-4}{x^4+x^3-4x^2-4}[/tex]The domain refers to all values of x for which the function is defined.The function is defined for[tex]x^4+x^3-4x^2-4\ne0[/tex]This implies that;[tex]x\ne -2.69,x\ne 1.83[/tex]b) The vertical asymptotes are x-values that makes the function undefined.To find the vertical asymptote, equate the denominator to zero and solve for x.[tex]x^4+x^3-4x^2-4=0[/tex]This implies that;[tex]x= -2.69,x=1.83[/tex]c) The roots are the x-intercepts of the graph.To find the roots, we equate the function to zero and solve for x.[tex]\frac{x^2-4}{x^4+x^3-4x^2-4}=0[/tex][tex]\Rightarrow x^2-4=0[/tex][tex]x^2=4[/tex][tex]x=\pm \sqrt{4}[/tex][tex]x=\pm2[/tex]The roots are [tex]x=-2,x=2[/tex]d) The y-intercept is where the graph touches the y-axis.To find the y-inter, we substitute;[tex]x=0[/tex] into the function[tex]f(0)=\frac{0^2-4}{0^4+0^3-4(0)^2-4}[/tex][tex]f(0)=\frac{-4}{-4}=1[/tex]e) to find the horizontal asypmtote, we take limit to infinity[tex]lim_{x\to \infty}\frac{x^2-4}{x^4+x^3-4x^2-4}=0[/tex]The horizontal asymtote is [tex]y=0[/tex]f) The greatest common divisor of both the numerator and the denominator is 1.There is no common factor of the numerator and the denominator which is  at least a linear factor.Therefore the function has no holes.g) The given function is a proper rational function. There is no oblique asymptote.See attachment for graph.