SOLUTION
We want to draw the graph of
[tex]g(x)=-2^x-1_{}[/tex]
The graph is shown below
Domain of the function.
The domain is determined from the x-axis. The function is defined for all values of x, hence the domain is negative infinity to positive infinity.
The domain in interval notation is
[tex]\mleft(-\infty\: ,\: \infty\: \mright)[/tex]
The Range of the funtion.
The range is determined from the y-axis. Looking at the graph, the graph has a horizontal asymptote drawn at y = - 1, and the y-values run below and does not exceed this -1, telling us it is between negative 1 and negative infinity.
Hence the range in interval notation is
[tex]\mleft(-\infty\: ,\: -1\mright)[/tex]
