Question

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

Answer 1

y = - f(x + 3)

Explanation:

First of all (and the easiest part of this) is just to look at the dotted lined graph. It is upside down. That means that y = - f(x). In other words, you just add a minus sign to f(x) and that will turn it upside down.

Now you want to shift it 3 units left. That means that inside f(x) you must do something to the x. To move it left, you add 3 to the x which is about as anti-intuitive as you can get, but it is also the right answer.

y = -f(x + 3)