Problem 14 · 2011 Math Kangaroo
Hard
Algebra & Patterns
How many of the functions \(y=x^{2}\), \(y=-x^{2}\), \(y=+\sqrt{x}\), \(y=-\sqrt{x}\), \(y=+\sqrt{-x}\), \(y=-\sqrt{-x}\), \(y=+\sqrt{|x|}\), \(y=-\sqrt{|x|}\) have graphs that appear in the sketch on the right?
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Answer: D — 6
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Hint 1 of 2
Sort the eight functions into square-type parabolas and square-root-type curves.
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Hint 2 of 2
The sketch shows the sideways square-root branches, not the upward/downward parabolas.
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Approach: match the sketch to the square-root family of curves
- The drawing shows curves that flatten near the axis like square roots, meeting at the origin.
- Six of the listed functions (the √-type ones) reproduce exactly those branches; the two parabolas do not.
- So 6 of the graphs appear.
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