Question

The graph of g(x) is f(x) translated to the left 8 units and up 2 units. What is the function rule for g(x) given f(x) =x^2

Answer 1

g(x) = (x+8)^2 + 2

verify by graphing both parabolas

Answer 2

Thank you!

Answer 3

[AI-generated answer — Explain Bot]

To find the function rule for g(x) given f(x) = x^2, we need to perform the given transformations:

1. Translation to the left by 8 units: To shift the function f(x) to the left, we subtract the desired amount from x. Therefore, g(x) = f(x + 8).

2. Translation up by 2 units: To shift the function up, we add the desired amount to the function itself. Since f(x + 8) is translated up by 2 units, the final function rule for g(x) is g(x) = f(x + 8) + 2.

Substituting f(x) = x^2 into the above equation, we get the function rule for g(x):

g(x) = (x + 8)^2 + 2.