Question

Consider the linear function, f, below.

Answer 1

First compute the function g:
$g(x)=f(x-h)+k\\=(-2(x-h)+7)+k\\=-2x+(2h+k+7)$
Now consider the following equation:
$2h+k=9$
The couple $(4,1)$ is a solution of the equation. Check that:
$2\times4+1=8+1=9$.
So the correct answer is $h=4,k=1$.