Question

given the graph of y = f(x), shown as a red dashed curve, drag the movable blue point to obtain the graph of y = f(x - 2) - 4. provide your answer below:

Explanation:

Step1: Analyze horizontal shift

For the function $y = f(x - h)+k$, a positive $h$ value shifts the graph of $y = f(x)$ to the right. Here $h = 2$, so the graph of $y=f(x)$ shifts 2 units to the right.

Step2: Analyze vertical shift

A negative $k$ value in $y = f(x - h)+k$ shifts the graph downwards. Here $k=-4$, so the graph of $y = f(x)$ shifts 4 units down after the horizontal - shift.

Answer:

The blue - point should be moved 2 units to the right and 4 units down from its original position on the graph of $y = f(x)$.