Question 1061131
Your second function and the question seem more interesting.


{{{(x+9)/(x^2+2x+5)}}} has a sign change at x=-9.  Denominator is not factorable, and denominator is positive for all x values.


Think how the rational expression goes as x tends either toward negative infinity or toward positive infinity.  The denominator increases in size MORE THAN the numerator.  This function will become increasingly closer to 0 to the left, and become increasingly closer to zero to the right.  Horizontal asymptote is y=0.


{{{graph(300,300,-10,10,-10,10,(x+9)/(x^2+2x+5))}}}


Same thing closer look:
{{{graph(300,300,-9,9,-3,3,(x+9)/(x^2+2x+5))}}}