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

To translate the function \(f(x) = x^2\) left 8 units and up 2 units to obtain the function \(g(x)\), you need to make adjustments to the original function.

1. To shift the graph left by 8 units, you need to replace \(x\) with \(x + 8\).

2. To shift the graph up by 2 units, you need to add 2 to the entire expression.

So, the function rule for \(g(x)\) is:

\[g(x) = (x + 8)^2 + 2\]

This means that \(g(x)\) is \(f(x)\) shifted 8 units to the left and 2 units up.