Quandaries
and Queries 

Name: Justina Student Secondary Level Questions i cant figure out the range of this equation in interval form because the highest point seems to be a decimal. please help f(x) = x + sqrt(4x^{2}) The domain i think is [2,2] and the range is [2,? I've been stumped by this question it seems like forever. I can only find the length of the square's diagonal, which leads me nowhere, since there is a tiny space where the air duct meets the floor. The figure is just a square. Inside is inscribed a large circle and in one corner is a small circle. Help!! 

Hi Justina, You are correct, the domain is [2,2]. For the range, f(sqrt(2)) = 2*sqrt(2) and using calculus, this can be shown to be the maximal value. We have two suggestions for your second problem. One that uses coordinates.
And one that doesn't use coordinates.
Claude and Penny 

