Question

How does the graph of g(x)=(x-3)^3+4 compare to the parent function f(x)=x^3

Answer 1

Explanation:

Using translation concepts, it is found that the graph of f(x), compared to the graph of g(x) is:

Shifted 8 units to the right.

Shifted 4 units up.

The parent function is:

Finding g(x - a) is the equivalent to shifting the graph a units to the right, thus, since we have that , the graph is shifted 8 units to the right.

Adding a to the function is the same as shifting the graph up a units, and in this problem 4 is added, thus the graph was also shifted 4 units up.