Question

How does the graph of g(x) = (x − 2)3 + 6 compare to the parent function of f(x) = x3?

Answer 1

The graph of g(x) is the graph of f(x) translated 2 units to the right and 6 units up.

How does the graph of g(x) compare to the one of f(x)?

Here we have:

$f(x) = x^3\\\\g(x) = (x - 2)^3 + 6$

You can notice that if we take f(x), and we shift it 2 units to the right, we have:

g(x) = f(x - 2)

Then if we apply a shift upwards of 6 units, then we have:

g(x) = f(x - 2) + 3

Replacing f(x) by the cubic parent function, we have:

$g(x) = (x - 2)^3 + 6$

So we conclude that the graph of g(x) is the graph of f(x) translated 2 units to the right and 6 units up.

If you want to learn more about translations:

https://brainly.com/question/24850937

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