How come A=pie*r^2 is a direct variation? What if r becomes a negative number and its squared value is larger than that of a small positive number? I know that r can't be negative in a circle but still the function itself isn't a direct variation. Please explain.  

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Plotting many (r, A) values will give you a parabola if you use A = Πr^2.  This is true for positive and negative values of r.  The range will always be positive.  However, the area is directly related to the square of the radius, not to the radius alone.  If you take the radius value, square it and plot it in a graph with its associated area in ordered pairs ( r^2, A ) like this, you will end up with a straight line that passes through the point (0, 0) and that is what a direct variation does.  This graph will look like a V to you, not a parabola.  The range of this function is 0 to positive infinity so it is not a problem if the squared value is larger than that of a small positive number.