Given are a function and its derivatives. Use a complete pre$-$calculus and calculus analysis listed below to help you sketch a detailed graph for $f(x).$ You must clearly label all points such as intercepts, relative max, relative min, inflection points. You must also clearly display and label any asymptotes.

Function: $f(x)=\frac{10x^3}{x^2-1},f^{\text{'}}(x)=\frac{10x^2(x^2-3)}{(x^2-1{)}^2},f^{\text{'}\text{'}}(x)=\frac{20x(x^2+3)}{(x^2-1{)}^3}$

a$)$ Find Horizontal asymptotes.

b$)$ Find vertical asymptotes.

c$)$ Find x and y intercepts.

d$)$ Find interval where f is increasing and decreasing.

e$)$ Find interval where f is concaved up and concaved down.

f$)$ Find the relative extrema: $($max and min $)$

g$)$ State any inflection points.

h$)$ Sketch