Show a graph representing the equation f(x) = -|x| - 2

An absolute value graph is simply two straight lines leading to one point and going out to infinity in a "v" shape.  This is because the y value is the absolute value of the x value, meaning the y value is always positive.  For , the two components are lines from  and from from . The graph of  is shown in the first picture. 

As you probably know, the slope intercept form for a line is y=mx+b, where m is the slope and b is the y-intercept.  In the equation , the y-intercept is -2.  This moves the entire graph down two units.  Also, |x| is negative in this equation.  This flips the "v" over, making the graph appear as the second picture shows.