Using shifting concepts, it is found that function g is given by:
[tex]g(x) = \frac{x^2 - 4x - 12}{4}[/tex]
--------------
- Horizontally stretching a function f(x) a units is the same as finding [tex]f(\frac{x}{a})[/tex]
- Shifting a function f(x) a units to the left is the same as finding f(x - a).
- Shifting a function f(x) down a units is the same as finding f(x) - a.
--------------
The parent function is:
[tex]f(x) = x^2[/tex]
--------------
Horizontally stretching by a factor of 2.
[tex]f(\frac{x}{2}) = (\frac{x}{2})^2 = \frac{x^2}{4}[/tex]
--------------
Shifting left 2 units:
[tex]f(\frac{(x-2)}{2}) = \frac{(x - 2)^2}{4} = \frac{x^2 - 4x + 4}{4}[/tex]
--------------
Shifting down 4 units:
[tex]g(x) = f(\frac{(x-2)}{2}) - 4 = \frac{x^2 - 4x + 4}{4} - 4 = \frac{x^2 - 4x + 4}{4} - \frac{16}{4} = \frac{x^2 - 4x - 12}{4}[/tex]
A similar problem is given at https://brainly.com/question/24465194
