Which statement best describes g(x) = cube root x + 6 - 8 and the parent function f(x) = cube root X?

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)

c on edge

Step-by-step explanation:

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Step-by-step explanation: