Question

The graph of f(x) = (0.5)x is replaced by the graph of g(x) = (0.5)x − k. If g(x) is obtained by shifting f(x) down by 2 units, the value of k is ___

Answer 1

k is the distance of the vertical translation.
Since you shifted the graph 7 units down, k will be equal to 7
So g(x) = (0.5)x - 7 is f(x) vertically translated 7 units down

If g(x) is obtained by shifting f(x) down by 7 units
meaning that
g(x)=(0.5)~~~~~7 units to the bottom from f(x)-k?

I can't explain but k=-7

it's g(x)=f(x)-(-7)
so the k=7.

f(x)-k=f(g)-7
the original function of f(x) is obtained by shifting f(g) 7 units down, or by -7
so x=7

Answer 2

`k = 2`

Explanation:

The value of k is:

`g(x) = 0.5\cdot x - k`

`f(x) - 2 = f(x) - k`

`k = 2`