Question

the function g (graphed below in blue) is a transformation of function f (graphed in black). what is the formula for function g in terms of f? draw (the graph is omitted here) \\(\circ\\ f(x) + 4\\) \\(\circ\\ f(x) - 4\\) \\(\circ\\ f(x + 4)\\) \\(\circ\\ f(x - 4)\\)

Explanation:

Step1: Identify vertical shift direction

Observe that every point on $g(x)$ is 4 units below the corresponding point on $f(x)$. A downward vertical shift of $k$ units is represented by subtracting $k$ from the original function.

Step2: Match to transformation rule

For a downward shift of 4 units, the transformation is $g(x) = f(x) - 4$.

Answer:

B. $f(x) - 4$