Question

Consider the function f(x) = x^2 – 3. Which transformation of f will result in the function g(x) = x² + 3?

Answer 1

To transform the function f(x) = x^2 - 3 into g(x) = x^2 + 3, a vertical shift upwards of 6 units is needed.

Step-by-step explanation:

The student has asked about the transformation of the function f(x) = x^2 - 3 that will result in the function g(x) = x^2 + 3. To transform f(x) into g(x), we need to apply a vertical shift of 6 units upwards.

This is because the graph of f(x) needs to be moved up so that the point where f(x) = 0 becomes the point where g(x) = 6, thus changing the -3 in the function f(x) to +3 in g(x).