Answer:
Here we can not see the options, so I will answer in a general way.
We have the equations:
g(x) = ∛(x + 6) - 8
f(x) = ∛x
First, let's describe the translations.
Vertical translation:
When we have a function f(x), a vertical translation of N units is written as:
g(x) = f(x) + N
Such that if N is positive, the translation is upwards
If N is negative, the translation is downwards.
Horizontal translation:
When we have a function f(x), a horizontal translation of N units is written as:
g(x) = f(x + N)
If N is positive, the translation is to the left
If N is negative, the translation is to the right.
Now that we know that, we can compare the functions:
g(x) = ∛(x + 6) - 8
f(x) = ∛x
So if we start with f(x), we can have a horizontal translation of 6 units to the left:
g(x) = f(x + 6)
And then a vertical translation of 8 units down:
g(x) = f(x + 6) - 8
∛(x + 6) - 8 = f(x + 6) - 8
Then g(x) is the function that you get when you apply a horizontal translation of 6 units to the left followed of a vertical translation of 8 units down to the function f(x)
