MathDB

f can be rotated/translated onto cf

Source: IMC 2007, Day 2, Problem 1

August 7, 2007

geometrygeometric transformationlogarithmsfunctionrotationIMCcollege contests

Problem Statement

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