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