Question

The graph of the parent function f(x)=x^3 is translated to from 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

(4, -7)

Step-by-step explanation:

In this exercise we have two functions:

`f(x)=x^3 \ and \\ \\ g(x)=(x-4)^3-7`

The figure below shows the graph of both functions. The graph of the function f has been plotted in red while the graph of the function g has been plotted in blue. As you can see, the graph of the function g has been shifted four units to the right and seven units downward. In other words, the point (0, 0) on the graph of f(x) corresponds to the point (4, -7) on the graph of g(x) and this is also shown in the figure below.