Question

Need the answer to number 8 pls

Answer 1

we can split it up into

$( \frac{x^4+2x^2}{x^2+2})+( \frac{1}{x^2+2} )= (\frac{x^2(x^2+2)}{x^2+2})+( \frac{1}{x^2+2} )x^2+\frac{1}{x^2+2}$
I see you were supposed to use synthetic division

not sure what the 'related function is'
but as |x| approaches positivie infinity, y approaches positive infinity
as |x| approaches negative infinity, y approaches positive infinity

for the original function
as x approaches positivie infinity $x^2+ \frac{1}{x^2+2}$ approaches positive infinity
as x approaches negative infinity $x^2+ \frac{1}{x^2+2}$ approaches positive infinity
this is due to the x^2 term making it positive