Question

Need help finding range of y = 2sin(x-3)

with step by steps ? ???

Answer 1

the sine function ranges in value from -1 to 1
so 2 sine has range twice that

-2 to 2

Answer 2

check this link
http://www.wolframalpha.com/input/?i=y+%3D+2sin%28x-3%29

Answer 3

@charlotteakina, does that make sense?

It wouldn't matter what you had inside the parenthesis, because that doesn't affect how "big" the sine function curve is. The sine curve normally ranges between -1 and 1, so it you multiply it by 2, you extend its range from -2 to 2.

Any coefficient to the sine has the same effect.

Answer 4

do you have the basic form showing a sine function with a, h, and k?

I can't recall how they show it... I can look it up, but if you have it handy, that would help.

Answer 5

Found it... Is this what you have?

y - k = A Sin B(x - h)

Answer 6

When you get a minute, check this link also... this is what I was using to refresh my memory:
http://home.windstream.net/okrebs/page83.html

So, the "k" is 0 in your problem... therefore there is no vertical shift.

Answer 7

y = 2sin(x-3)

y - k = A Sin B(x - h)

k = 0 <<--- no vertical shift
A = 2 <<--- increases range from -1,1 to -2,2
B = 1 <<-- no change in period
h = 3 <<--- shifts graph right by 3

Answer 8

So y = 2sin(x-3) will look like a normal sine curve, except the "ups" and "downs" will be twice as big, and the whole thing will be shifted right by 3 units.

If the equation had included a "k" term, like:
y - 5 = 2sin(x-3)

Then the shape of the curve would be the same as above, but it would be shifted vertically up by 5 units. This would change the range from -2,2 (a "swing" of 4) to 3,7 (still a swing of 4, but shifted up vertically 5 units).

Answer 9

I'm back.

I would simplify it a little.

That paragraph is just for your understanding... no need to put all that in, plus I was intentionally trying to talk in "plain terms" vs. "math terms".

Why don't you leave out the paragraph and use the other parts...

Answer 10

The question only asked about range, so it doesn't really matter that it shifts right. But if you have to answer about the A, h, and k parts, then the above explanation does address those aspects.

Go eat ;)