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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

Respuesta :

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

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