Answer:
y = In(x) - 5
Step-by-step explanation:
The translation is a geometrical transformation, that changes the location of a figure. In a function, the independent term exerts a role in the translation of the graph.
Algebraically, to translate the function by shifting down 5 units. We have to insert in the domain a value that will return to zero and add negative 5 units.
To satisfy this condition, all that's left is the first and the last option.
Let's test.
y = In(x-5)
[tex]y=log_{e} (x-5)\\ y=ln (1-5)\\ y=ln(-4)\\ y=[/tex]
There is no logarithm < 0
y = In(x) - 5
[tex]lnx=log_{e} x\\ y=log_{e}(x)-5\\ y=log_{e}(1)-5\\ y=0-5\\ y=-5[/tex]
So (1,-5) this is the first point after the curve leaves the y axis
Geometrically, Check the graph below.
