The domain (input values) of the sine function is:
2 answers:
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ANSWER
To graph the function
follow the steps below.
1. Find y- intercept by plugging in
.
is on the interval, 
, so we substitute in to
Hence the y-intercept is
2. Find x-intercept by setting
This implies that
on
or
on 
We now solve for
on each interval,
on
or
on
But observe that
does not belong to
This means it can never be an intercept for this piece-wise function.
Hence our x-intercept is
3. Plotting the boundaries of the interval.
For on
.
This point coincides with the x-intercept.
So we have the point
. But note that 
does not belong to this interval so we plot this point as a hole.
For
on
So we plot
So we plot
also as a hole.
Plotting all these points we can now graph the function,
See attachment for graph.
To graph the function
follow the steps below.
1. Find y- intercept by plugging in
Hence the y-intercept is
2. Find x-intercept by setting
This implies that
or
We now solve for
or
But observe that
This means it can never be an intercept for this piece-wise function.
Hence our x-intercept is
3. Plotting the boundaries of the interval.
For
This point
So we have the point
For
So we plot
So we plot
Plotting all these points we can now graph the function,
See attachment for graph.