$y=f(x)$ is continuous and defined for all $x$ real numbers.
Point $A(0,f(0))$ is to be moved to on x axis while $f(x)$ is rigid curve and the rigid curve always passes on point $B (x_1,f(x_1))$ as well. How can the transformed new curve be defined ?
Thanks a lot for answers and advice how to start.
EDIT: An Example: if $f(x)=ax$ then after the transformation : $f(x)$ will turn $g(x)=ax_1(x−α)/(x_1−α)$ where $α$ is transformation parameter.