The function is
.
The above function is in the form
.
Here A is amplitude, B is stretch along x-axis, d is a constant determines the vertical shift.
\The amplitude of the function is
.
1)
\The period of a sine function is given by
.
In the given function B is 2.
\So, the period is
.
2)
\Phase shift of a function is given by
.
In the given function c is
.
Phase shift is
.
3)
\In the given function d is zero, that means there is no vertical shift in the function.
\4)
\To find the asymptotes of the function, graph the function over a period.
\The solutions of the given functions are
\
.
Taking
as an interval difference plot the graph. \ \
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Now plot these points
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Since sine function is a continues sinusoidal function.
\So, it has no vertical asymptotes.
\And horizontally it is oscillating between
, but it is not converging at either
.
So, it also doesn\\'t have horizontal asypmtotes.
\5)
\From the graph we can also say the domain and range of the function.
\Domain is
.
It is oscillating between
, so the range is
.