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
f(x)=x^2 to the left 8 units ----> (x+8)^2
then up 2 units ----> (x+8)^2 + 2
To find the function rule for g(x) if it is a translation of f(x), we can start by examining the translation process.
We have been told that f(x) is translated to the left 8 units and up 2 units to obtain g(x).
First, let's consider the translation to the left. When a function is translated to the left, the x-values are decreased by the specified amount. In this case, f(x) is translated 8 units to the left, so we subtract 8 from x.
Next, let's look at the translation upward. When a function is translated upward, the y-values are increased by the specified amount. In this case, f(x) is translated 2 units upward, so we add 2 to y.
Combining these two translations, we can write the function rule for g(x) as follows:
g(x) = f(x - 8) + 2
Since f(x) is given as x^2, we can replace f(x) with x^2 in the function rule:
g(x) = (x - 8)^2 + 2
So, the function rule for g(x) is g(x) = (x - 8)^2 + 2.