Question 709291
Some help with #1, the rational function.


The numerator and the denominator are factorable.

{{{R(x)=((x+6)(x-5))/((x+4)(x-5))}}}


The graph will be much like {{{f(x)=(x+6)/(x+4)}}} but will not contain a value for x=5.  x is undefined at 5.  Watch carefully also that x cannot equal -4 so there is a (vertical asymptote) at x=-4.  As x tends toward either negative infinity or positive infinity, R approaches the value of 1.