Question

If we shift the function f(x)=x2+4 five units downward, what is true about the resulting transformed function, g(x)?

a) The vertex is shifted left.
b) The vertex is shifted right.
c) The vertex is shifted downward.
d) The vertex remains unchanged.

Answer 1

The resulting transformed function g(x) will have its vertex shifted downward.

Step-by-step explanation:

When we shift a function f(x) = x^2 + 4 five units downward, the resulting transformed function g(x) is obtained by subtracting 5 from the original function:

g(x) = f(x) - 5

So, the vertex of the resulting transformed function will be shifted downward by 5 units. The vertex of the original function f(x) = x^2 + 4 is at (0, 4), and after shifting downward, the vertex of the transformed function will be at (0, -1).

Therefore, the correct answer is c) The vertex is shifted downward.