Chapter 1 - Section 1.6 - Transformations of Functions - Exercise Set - Page 241: 16

See graph and explanations.

Using the graph in the exercise, given the line segment of $y=f(x)$, we can obtain the new line segment of $g(x)=-f(2x)-1$ by first compressing the original horizontally to one half, reflecting the result around the x-axis and then shifting it down 1 unit (shown as the new red line segment in the figure).