Question

How does the graph of g(x) = (x − 4)3 + 5 compare to the parent function f(x) = x3?

A g(x) is shifted 4 units to the right and 5 units up.
B g(x) is shifted 5 units to the right and 4 units up.
C g(x) is shifted 4 units to the left and 5 units up.
D g(x) is shifted 5 units to the right and 4 units down.

Answer 1

Answer: its option A

Answer 2

Explanation:

The graph of g(x) = (x − 4)^3 + 5 is obtained by taking the parent function f(x) = x^3 and making transformations.

1. The (x − 4) term inside the parentheses represents a horizontal shift of 4 units to the right.

2. The "+ 5" outside the parentheses represents a vertical shift of 5 units up.

So, the correct answer is:

A) g(x) is shifted 4 units to the right and 5 units up.