Question

Can anyone explain how's 'D' the answer?

http://prntscr.com/bs1305

Answer 1

If you start with function y = f(x), you get a certain grpah.
That is shown in the large graph to the left.

Answer 2

Now you are asked to find out which of the 4 small graphs corresponds to
g(x), when you are told that g(x) = -f(x) + 1

Answer 3

Think of the first graph, y = f(x)
Now look at g(x), but for now look only at the part in red below:

\(g(x) = \color{red}{-f(x)} + 1\)

Answer 4

What does the y-coordinate of each point in -f(x) look like
compared to the corresponding y-coordinate of f(x)?

Answer 5

I think it means -1

Answer 6

You're on the right track.
It actually -1 times each y-coordinate.

Answer 7

Notice that in the given graph of y = f(x),
every point of y = f(x) has the same y-coordinate, -3.
You see how y = f(x) is a horizontal segment?
That shows that every y-coordinate of y = f(x) is the same, and it happens to be -3.

Answer 8

Now think of g(x).
g(x) = -f(x) + 1

The part g(x) = -f(x) means that every y-coordinate of g(x) is the the same as each corresponding coordinate of f(x) multiplied by -1.

In our case, g(x) is not simply g(x) = -f(x).
We are given
g(x) = -f(x) + 1
That means, take every y-coordinate of f(x) which is -3.
Then multiply it by -1 to make it 3.
Then add 1 to it to make it 4.
That is why g(x) = -f(x) + 1 ends up with every y-coordinate equal to 4.