Answer:
The resulting function is [tex]g(x) = \log_{2} (x+5)-4[/tex].
Step-by-step explanation:
Let [tex]f(x)[/tex] a real function, we define the following function operations:
Horizontal translation
[tex]g(x) = f(x + a)[/tex] (1)
If [tex]a > 0[/tex], then horizontal translation is to the left, otherwise it is to the right.
Vertical translation
[tex]g(x) = f(x) + a[/tex] (2)
If [tex]a> 0[/tex], then vertical translation is upwards, otherwise it is downwards.
Knowing that [tex]f(x) = \log_{2}x[/tex] and [tex]g(x)[/tex] is the result of translating [tex]f(x)[/tex] four units downwards and five units to the left. Then, we find that:
[tex]g(x) = \log_{2} (x+5)-4[/tex]
The resulting function is [tex]g(x) = \log_{2} (x+5)-4[/tex].
