Question

Can you help graph abs give the domain and range

Answer 1

We want to draw the graph of

`g(x)=-2^x-1_{}`

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

`\mleft(-\infty\: ,\: \infty\: \mright)`

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

`\mleft(-\infty\: ,\: -1\mright)`