Question

Let's f(x)=2x-5 . Write a function k whose graph is a rotation of f(x)about (0,-5) by a factor of 1/2.

Answer 1

$f(x)=2x-5$

the graph

the new line must pass through the point so we can just multiply x by the factor

$\begin{gathered} k(x)=2x(\frac{1}{2})-5 \\ k(x)=x-5 \end{gathered}$

red is the rotation and the green line is the solution (x-5)