Question

7: please help! please only real answers; will report

Answer 1

The resulting function is
`g(x) = \log_(2) (x+5)-4`.

Explanation:

Let
`f(x)` a real function, we define the following function operations:

Horizontal translation

`g(x) = f(x + a)` (1)

If
`a > 0`, then horizontal translation is to the left, otherwise it is to the right.

Vertical translation

`g(x) = f(x) + a` (2)

If
`a> 0`, then vertical translation is upwards, otherwise it is downwards.

Knowing that
`f(x) = \log_(2)x` and
`g(x)` is the result of translating
`f(x)` four units downwards and five units to the left. Then, we find that:

`g(x) = \log_(2) (x+5)-4`

The resulting function is
`g(x) = \log_(2) (x+5)-4`.