Question

The graph of f(x) = (0.5) is replaced by the graph of g(x) = (0.5)* - k. If g(x) is obtained by shifting f(x) down by 3 units, then what is the value of k?

Ok=-3
Oka-
O
OK= 1/3
Ok = 3

Answer 1

`k = 3`

Explanation:

Given

`f(x) = 0.5x`

`g(x) = 0.5x - k`

Required

`Find\ k`

Initial expression of f(x) is
`f(x) = 0.5x`

From the question; we understand that f(x) was shifted down by 3 units;

This implies that

`New\ f(x) = 0.5x - 3`

Also from the question; we understand that this new f(x) is equivalent to g(x);

In other words;

`New\ f(x) = g(x)`

Substitute
`New\ f(x) = 0.5x - 3` and
`g(x) = 0.5x - k`

This gives

`0.5x - 3 = 0.5x - k`

Subtract 0.5x to both sides

`0.5x - 3 - 0.5x = 0.5x - k - 0.5x`

Rearrange

`0.5x - 0.5x - 3 = 0.5x - 0.5x- k`

`-3 = -k`

Multiply both sides by -1

`-3 * -1 = -k *-1`

`3 = k`

`k = 3`