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 \(y=|x|\), the two components are lines \(y=-x\) from \((- \infty,0]\) and \(y=x\) from from \([ 0,\infty)\). The graph of \(y=|x|\) 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 \(f(x)=-|x|-2\), 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.
