Question

What happens to the function f(x) = x4 when it becomes f′(x) = x4+5?

a) It moves 5 units to the right.
b) It moves 5 units to the left.
c) It moves 5 units downward.
d) It moves 5 units upward.

Answer 1

The function f(x) = x^4, when transformed to f'(x) = x^4 + 5, moves 5 units upward on the graph.

Step-by-step explanation:

When the function f(x) = x4 is changed to f'(x) = x4 + 5, it represents a vertical shift of the graph of the original function. Specifically, every point on the graph of f(x) is moved 5 units upward, because the constant 5 is added to the output (y-value) of the function for all x. The correct answer to what happens to the function when it becomes f'(x) = x4 + 5 is d) It moves 5 units upward.