Question 1059941
f(x)=(3x-7)/(x+1)


{{{f(x)=(3x-7)/(x+1)}}}


Zero at  {{{7/3}}} and undefined at {{{x=-1}}}.

<pre>
INTERVAL                 EXAMPLE x      SIGN OF f(x)
{{{-infinity<x<-1}}}                -3            (-)/(-)=(+), positive
{{{-1<x<=7/3}}}                   0            (-)/(+)=(-), negative
{{{7/3<=x<infinity}}}                   4            (+)/(+)=(+), positive
</pre>

The function has a horizontal asymptote of y=3.

Will f(x) ever be {{{3}}} ?
{{{3x-7=3(x+1)}}}
{{{3x-7=3x+3}}}----impossible to solve this.  No solution.


RANGE:  The real numbers such that {{{system(-infinity<y<3,AND,3<y<infinity)}}}
DOMAIN:  Set of real numbers such that  {{{system(-infinity<x<-1,AND,-1<x<=7/3,AND,7/3<=x<infinity)}}}



{{{graph(350,350,-12,6,-6,12,(3x-7)/(x+1))}}}