Question

What is the range of the function y = 1 + 2sin(x -pi )?

Answer 1

is this a polar equation or a cartesian one?

Answer 2

ahh idk but here are the answers A. -1 to 1 B. -2 to 2 C. 0 to 3 D. -1 to 3 E. -3 to 3

Answer 3

Just remember that sin... no matter what is inside, always has a range of -1 to 1.

Answer 4

so is it -1 to 1

Answer 5

Of course not :)
That's only for the sin(x-pi) part.
So if sin goes from -1 to 1.
From where to where does 2sin(x - pi) go?

Answer 6

-2 to 2

Answer 7

That's good :)
Now there's a 1 + at the left.
So add one to both of these endpoints, you get?

Answer 8

i really have no idea

Answer 9

-2 to 2 is correct for the 2sin(x - pi) part.
Now, there's a 1 + part along with it
1 + 2sin(x - pi)
this is the same as
2sin(x - pi) + 1

The 2sin(x - pi) goes from -2 to 2.
So if you add 1, it will then go from...?

Answer 10

-3 to 3

Answer 11

why -3?
You add 1 not subtract :P

Answer 12

so if you add would you get 3 to 2

Answer 13

Okay... range of 2sin(x-pi) is [-2 , 2]
So if we add 1 to the function, then we add 1 to the endpoints of the range.
[-2 + 1 , 2 + 1]
Which gives...?

Answer 14

-1 to 3

Answer 15

There you go.

Answer 16

thanks man