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UKMT Senior Mathematical Challenge, 2025

Algebra Difficulty 3.0 AMC 10/12 Prove it United Kingdom

The output of the function $F(x)$ when applied to a real number $x$ is the greatest integer less than or equal to $x$ . For example, $F(3) = 3$ , $F(4.7) = 4$ , $F(-2.3) = -3$ . Which of the following is the graph of $y = x^{F(x)}$ for non-zero values of $x$ in the interval $-2 < x < 2$ ?

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