– the asymptotes are the set of
–
values or
values
that the graph cannot take.If
then
since
that would mean dividing by 0, and
since
These
equations can also be obtained from the form
by
considering the denominator
which
may not take the value 0, so
and
the coefficient ofin
numerator and denominator. Letting
gives
In
fact if
the
equation of theasymptote
is given by dividing the coefficient ofin
numerator and denominator to give
Example:
The
equation of the x asymptote is
and
the equation of the
asymptote is given by
Sketching
the graph can be aiding by finding the intercepts with the
axes.
and
The
graph is sketched below.
which
rounds down ro 3.
less
than or equal to
find
as
a mixed fraction or decimal and round the answer down to the nearest
whole number.
which
rounds down to 33, so there are 33 multiples of 3 less than 100.
and
common difference
so
we can use the formula for the sum of an arithmetic sequence,
giving
indicates
the result of the division
and
asked to find the set of values of
for
which
or
We
could have factorised the
to
obtain
and
solved
to
obtain
hence
the set of values of
is
1 which is positive, we know it will be a “bum” curve,so the set
of solutions for
We
are asked for example to find the set of values of
We
can see from the graph that there is only one set of values:
We
could have factorised the expression for
and
solved
to
obtain
hence
we could write down the set of values of
We
are asked
The
curve is a “breast” curve and we can read off the solutions
and
solve
hence
finding the set of solutions just given.