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?
g(x) = f(x+8)+2 = (x+8)^2+2
so that is the answer
umm technically that is the answer
thanks steve<3
Steve is right. This isn't an equation you need to "solve" it's mostly just something to know.
To find the function rule for g(x) given the graph of f(x) = x² translated to the left 8 units and up 2 units, we need to consider the effects of the horizontal and vertical translations on the original function.
1. First, let's address the horizontal translation. Translating the function to the left means shifting the graph to the right. Since g(x) is translated to the left 8 units, we need to replace x with (x + 8) in the function rule.
2. Next, let's consider the vertical translation. Translating the function up means shifting the graph vertically. In this case, g(x) is translated up 2 units, so we need to add 2 to the function rule.
Combining these two transformations, the function rule for g(x) can be computed as follows:
g(x) = f(x) translated left 8 units + up 2 units
= (x + 8)² + 2
Therefore, the function rule for g(x) given f(x) = x² and the specified translations is g(x) = (x + 8)² + 2.