Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 1 - Precalculus Review - 1.1 Real Numbers, Functions, and Graphs - Exercises - Page 12: 86

Answer

$f(x)= (x-a)^3$ (other answers are possible.)

Work Step by Step

We need to find a function that is symmetric with respect to the point $(a,0)$. We know that the odd cubic function $f(x)=x^3$ is symmetric with respect to the origin $(0,0)$. If we shift this function by $a$ units to the right, we will obtain the desired function. That is, the function $f(x)= (x-a)^3$ is symmetric with respect to $(a,0)$.
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