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how does the graph of f(x) = (x − 8)3 + 4 compare to the parent function g(x) = x3?

The function is the function translated right by 8 units and up by 4 units

Step-by-step explanation:

We can express as . So each input value x to the function g is shifted left by 8 units. This has the effect of shifting the graph of the function g right by 8 units. Because think about it. Given some x location to find f(x), we're effectively saying "see the value of g(x) 8 units to the left of here". So g(x - 8) expresses shifting the graph of f to the right by 8 units. (If we were to have g(x + 8), it would shift the graph of f left 8 units).

Now, to every output of g(x - 8), we add 4. This means that each output of the function g(x - 8) is shifted up four units.

The combination of these two shifts produces a translation of 8 units to the right, and 4 units up.

i think the correct option is the second option.