Give the details of each characteristic for the following functions

a$.$ Domain of the function

b$.$ x$-$ and y$-$intercepts

c$.$ Symmetry

d$.$ End behavior $($limits at $$ & $-f(x)=2x^3+2x+1$

$f(x)=\frac{2(x^2-9)}{x^2-4}$

$f(x)=\frac{x}{\sqrt[\phantom{2}]{x^2+2}}$

$f(x)=\frac{2x^3}{x^2+1}$

$f(x)=\frac{1}{1+x^2}$

$f(x)=\frac{1}{1-x^2}$

$f(x)=\frac{x^2+1}{x^2-1}$

$f(x)=\frac{4(x-1{)}^2}{x^2-4x+5})$ including

horizontal or slant asymptotes

e$.$ Vertical Asymptotes

f$.$ Differentiability

g$.$ Intervals of increase and decrease

h$.$ Local maximums and local minimums

i$.$ Intervals of upward or downward

concavity

j$.$ Inflection points