Question 166029
Let's look at the function first.
{{{f(x)=(x+4)/(x-1)}}}
It is undefined at x=1 (because of division by zero).
.
.
.
As you approach x=1 from the left, the numerator is positive, the denominator is negative, f(x) goes to negative infinity.
.
.
.
As you approach x=1 from the right, the numerator is positive, the denominator is positive, f(x) goes to positive infinity.
.
.
.
As x grow large (negative or positive), the function looks like,
{{{f(x)=x/x=1}}}
So there is a horizontal asymptote at y=1.
.
.
.
f(x) crosses the x-axis when f(x)=0
{{{f(x)=(x+4)/(x-1)=0}}}
{{{x+4=0}}}
{{{x=-4}}}
f(x) cross the x-axis when x=-4.
.
.
.
f(x) crosses the y-axis when x=0
{{{f(x)=(x+4)/(x-1)=0}}}
{{{(0+4)/(0-1)=-4}}}
{{{y=-4}}}
f(x) crosses the y-axis when y=-4.
.
.
.
{{{ graph( 300, 300, -50, 50, -2, 2, 1,(x+4)/(x-1))}}}