ANSWER
[tex]g(x) = {x}^{2} + 4x + 4[/tex]
EXPLANATION
The given function is
[tex]f(x) = {x}^{2} - 6x + 9[/tex]
This can be rewritten as:
[tex]f(x) = {(x - 3)}^{2} [/tex]
If this function is shifted 5 units to the left to create g(x), the
[tex]g(x) = f(x + 5)[/tex]
We substitute x+5 into f(x) to get:
[tex]g(x) = {(x + 5 - 3)}^{2} [/tex]
[tex]g(x) = {(x + 2)}^{2} [/tex]
We expand to get:
[tex]g(x) = {x}^{2} + 4x + 4[/tex]
Answer:
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
