Question

The graph of y = f(x) is the solid black graph below. Which function represents the dotted graph? ​

Answer 1

y = -f(x - 5)

Explanation:

the function of the dotted graph is f(x) shifted (or translated) 5 units to the right and then reflected across the x-axis.

shifting it to the right is happening by reducing every x value by 5 (so that we get for x the functional value of x-5).

and reflecting it across the x-axis simply means to flip the sign. everything that was originally above the x-axis is now with the same distance below the x-axis (and vice versa).

therefore, the new

y = -f(x - 5)