Question

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

Answer 1

Answer:

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

Step-by-step 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 $g(x) = \log_{2} (x+5)-4$.