Find the function rule for g(x). The function f(x) = x2 . The graph of g(x) is f(x) translated to the right 8 units and down 7 units. What is the function rule for g(x)?

g(x) = f(x-8)-7

To find the function rule for g(x), which is the graph of f(x) translated to the right 8 units and down 7 units, we can apply these two transformations to the original function rule f(x) = x².

1. Translation to the right: To translate a function to the right a certain number of units, we need to subtract that number from the input variable. In this case, we want to translate f(x) 8 units to the right, so we subtract 8 from the input variable x: g(x) = f(x - 8).

2. Translation down: To translate a function downward, we subtract a constant value from the output variable. Here, we want to translate g(x) down 7 units, so we subtract 7 from the equation: g(x) = f(x - 8) - 7.

Since the original function f(x) is given as f(x) = x², we substitute this into our equation for g(x):
g(x) = (x - 8)² - 7.

Therefore, the function rule for g(x) is g(x) = (x - 8)² - 7.

To find the function rule for g(x), we need to determine how the graph of f(x) has been translated to obtain the graph of g(x).

The translation states that the graph of g(x) is obtained by translating the graph of f(x) 8 units to the right and 7 units down.

To translate a function to the right, we replace the variable x with (x - a), where a represents the amount of units the function is translated to the right. To translate a function down, we subtract the amount of units from the function.

So, to express the translation of f(x) to obtain g(x), we can write the function rule for g(x) as:

g(x) = (x - 8)^2 - 7

Therefore, the function rule for g(x) is g(x) = (x - 8)^2 - 7.