Question

Identify the equation that translates Y = In(x) five units down

Answer 1

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)

$y=log_{e} (x-5)\\ y=ln (1-5)\\ y=ln(-4)\\ y=$

There is no logarithm < 0

y = In(x) - 5

$lnx=log_{e} x\\ y=log_{e}(x)-5\\ y=log_{e}(1)-5\\ y=0-5\\ y=-5$

So (1,-5) this is the first point after the curve leaves the y axis

Geometrically, Check the graph below.

Answer 2

Y=ln(x)-5 because when shifting down you look at the number outside parenthesis