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) = x2 ?
To translate the graph of f(x) = x^2 to the left 8 units, we substitute x with (x + 8). To translate the graph up 2 units, we add 2 to the function. Therefore, the function rule for g(x) is g(x) = (x + 8)^2 + 2.
To translate the graph of f(x) to the left 8 units, we need to subtract 8 from x. To translate it up 2 units, we need to add 2 to the function. Therefore, the function rule for g(x) can be given as:
g(x) = f(x - 8) + 2
Since f(x) = x^2, we can substitute it in the function rule:
g(x) = (x - 8)^2 + 2
So, the function rule for g(x) given f(x) = x^2 is g(x) = (x - 8)^2 + 2.
To find the function rule for g(x), given f(x) = x^2, we need to apply the given translations: translate f(x) to the left by 8 units and up by 2 units.
First, let's consider the translation to the left. To shift a function to the left by a certain number of units, we subtract that number of units from x. Therefore, to shift f(x) to the left by 8 units, we replace x with (x + 8).
Now let's consider the translation up by 2 units. To shift a function up by a certain number of units, we add that number to the function. Therefore, to shift (x + 8) by 2 units up, we add 2 to the function.
Combining both translations, the new function g(x) in terms of f(x) is:
g(x) = f(x + 8) + 2.
Substituting f(x) = x^2 into the equation, we get:
g(x) = (x + 8)^2 + 2.
Therefore, the function rule for g(x) is: g(x) = (x + 8)^2 + 2.