Question

What is the equation of the translated function, g(x), if f(x) = x²?

Answer 1

To translate the function f(x) = x² to create a new function, g(x), adjustments along the x or y axis are needed. For instance, if the function is translated 2 units to the right and 3 units up, g(x) would be represented by the equation g(x) = (x-2)² + 3.

Step-by-step explanation:

The equation f(x) = x² is a standard parabolic function. In order to translate this function to create a new function, g(x), shifts along the x or y axis would need to be made. For example, if we were to translate the function 2 units to the right and 3 units upwards, the new function would be represented as g(x) = (x-2)² + 3.

Here's a step-by-step explanation:

1. When we translate the function to the right by 2 units, we replace 'x' in the equation f(x) = x² with '(x-2)'.
2. So, the equation becomes f(x) = (x-2)².
3. When we translate the function upwards by 3 units, we add '3' to the equation. So, the new equation becomes g(x) = (x-2)² + 3.

Learn more about Function Translation