22. 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? (2 points)
To find the function rule for g(x) given f(x) = x², we need to apply the given translations to the function f(x). We can achieve this by modifying the original function rule.
To translate a function to the left, we need to replace x with (x + a), where 'a' represents the number of units to shift. In this case, we need to shift it 8 units to the left, so we replace x with (x + 8).
To translate a function up, we need to add a constant value to the function. In this case, we need to shift it 2 units up, so we add 2 to the function.
Combining these two transformations, we now have the new function rule for g(x):
g(x) = f(x + 8) + 2
Since f(x) = x², we can replace f(x) with x² in the function rule:
g(x) = (x + 8)² + 2
Therefore, the function rule for g(x) is g(x) = (x + 8)² + 2.