The function f (x) = x - 6x + 9 is shifted 5 units to the left to create g (x). What is

g (x) = x^2 + 4x + 4

Step-by-step explanation:

In translation of functions, adding a constant to the domain values (x) of a function will move the graph to the left, while subtracting from the input of the function will move the graph to the right.

Given the function;

f (x) = x2 - 6x + 9

a shift 5 units to the left implies that we shall be adding the constant 5 to the x values of the function;

g (x) = f (x+5)

g (x) = (x+5) ^2 - 6 (x+5) + 9

g (x) = x^2 + 10x + 25 - 6x - 30 + 9

g (x) = x^2 + 4x + 4