You can
put this solution on YOUR website!The horizontal asymptote tells you, roughly, where the graph will go when x is really, really big.
When the degrees of the numerator and the denominator are the same, then the horizontal asymptote is found by dividing the leading terms, so the asymptote is given by:
y = (numerator's leading coefficient) / (denominator's leading coefficient)
This is
.
………… this function has degree-1 polynomials top and bottom; the degrees are the same in the numerator and the denominator
Since the degrees are the same, the numerator and denominator "pull" evenly; this graph should not drag down to the
, nor should it shoot off to infinity.
Again, think in terms of
values for
.
When
is really
, you'll have, roughly, 5 times something big divided by once something big (minus a 1) so you'll roughly have
, which reduces to just
so,
for this is
-->
...
-->
-->
...
-->
correspond to the
of the
of a rational function.
So, set the denominator of the above fraction equal to zero and solve, this will tell me the values that
cannot be:
………..so,
cannot be
, because then I'd be dividing by zero
If you graph it, you will see how the graph avoid the line
(