Question

The graph of the parent function f(x) = x3 is translated to form the graph of g(x) = (x − 4)3 − 7. The point (0, 0) on the graph of f(x) corresponds to which point on the graph of g(x)?

Answer 1

Answer:4, -7

Explanation:

Answer 2

The point (0, 0) in the graph of f(x) corresponds to the point (4, -7) in the graph of g(x)

Explanation:

Notice that when we start with the function
`f(x)=x^3`, and then transform it into the function:
`g(x)=(x-4)^3-7`

what we have done is to translate the graph of the function horizontally 4 units to the right (via subtracting 4 from the variable x), and 7 units vertically down (via subtracting 7 to the full functional expression).

Therefore, the point (0, 0) in the first function, will now appeared translated 4 units to the right (from x = 0 to x = 4) and 7 units down (from y = 0 to y = -7).

then the point (0, 0) after the translation becomes: (4, -7)