IMC / 2007 / Problems / Day 2, P7

IMC 2007 · Day 2 · P7

medium

Let $f : \mathbb{R} \to \mathbb{R}$ be a continuous function. Suppose that for any $c > 0$ , the graph of $f$ can be moved to the graph of $cf$ using only a translation or a rotation. Does this imply that $f(x) = ax + b$ for some real numbers $a$ and $b$ ?

Solution (official)

No. The function $f(x) = e^x$ also has this property since $c e^x = e^{x + \log c}$ .

How the field did

contestants scored

242

average (of 20)

9.87

solved (≥ 80%)

48.8%

near-0 (≤ 10%)

50.0%

discrimination

0.44

Score distribution (field cohort)

Computed on contestants with a meaningful total (field cohort); discrimination is the corrected item–total correlation.

IMC 2007 · Day 2 · P7

How the field did

Score distribution (field cohort)

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