Question

Find g(x), where g(x) is the translation 1 unit up of f(x) = x?.

Write your answer in the form a(x - h)? + k, where a, h, and k are integers.

Answer 1

To translate the function f(x) = x^2 up by 1 unit, you add 1 to the function, which gives g(x) = x^2 + 1. In the form a(x - h)^2 + k, this is written as g(x) = 1(x - 0)^2 + 1.

Step-by-step explanation:

The given function is f(x) = x^2. A translation of this function 1 unit up would mean adding 1 to the function value, that is, to the y-coordinate. This gives us a new function g(x), which is f(x) + 1. Thus the new function is g(x) = x^2 + 1.

Translating f(x) 1 unit up does not affect the x-coordinate (h) or the compression (a) of the graph, so those remain the same. The form of a translated function is a(x - h)^2 + k, where 'k' is the vertical translation. Since we are translating up by 1 unit, our 'k' is 1. Therefore, the answer in the requested form is g(x) = 1(x - 0)^2 + 1 or simply g(x) = x^2 + 1.