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

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A386idn
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.
View image A386
View image A386
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