Question

Consider the linear function, f, below.

f(x) = - 2x + 7

If g(x) = f(x - h) + k, what are the possible values of h and k such that the graph of function g is 9 units below the graph of function f?

h = -5 and k = 1

h = 4 and k = 1

h = -2 and k = 2

h = -9 and k = 2

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*4+1=8+1=9`.
So the correct answer is
`h=4,k=1`.