Question

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

O y = In(x-5)
O y = In(x)+5
o y = In(x+5)
o y = In(x) - 5

Answer 1

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

Answer 2

y = In(x) - 5

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.