Question

The function f(x) = x2 - 6x + 9 is shifted 5 units to the left to create g(x). What is
g(x)?

Answer 1

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

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

Answer 2

`g(x) = {x}^(2) + 4x + 4`

EXPLANATION

The given function is

`f(x) = {x}^(2) - 6x + 9`

This can be rewritten as:

`f(x) = {(x - 3)}^(2)`

If this function is shifted 5 units to the left to create g(x), the

`g(x) = f(x + 5)`

We substitute x+5 into f(x) to get:

`g(x) = {(x + 5 - 3)}^(2)`

`g(x) = {(x + 2)}^(2)`

We expand to get:

`g(x) = {x}^(2) + 4x + 4`