the graph of ( y = f(x) ) is the solid black graph below. which function represents the dotted…

Explanation:

Step1: Analyze the horizontal shift

The general rule for horizontal shift of a function (y = f(x)) is: if the graph shifts (h) units to the left, the function becomes (y=f(x + h)); if it shifts (h) units to the right, the function becomes (y = f(x - h)). The dotted graph is shifted 4 units to the left of the solid - black graph (y = f(x)). So, the (x) - value in the function changes as (x\to x + 4), and the function part is (y=f(x + 4)).

Step2: Analyze the vertical shift

The general rule for vertical shift of a function (y = f(x)) is: if the graph shifts (k) units up, the function becomes (y=f(x)+k); if it shifts (k) units down, the function becomes (y = f(x)-k). The dotted graph is shifted 1 unit up from the position after the horizontal shift. So, the function becomes (y=f(x + 4)+1).

Answer:

(y = f(x + 4)+1)