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How do I find the range of the function. #y=2+sinx#?

Answer 1

Sadie Alexander

We know

#-1 le sinx le 1#.

By adding 2 to everyone,

#1 le 2+sinx le 3#.

Hence, the range is #[1,3]#.

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Answer 2

Serenity Johnson

To find the range of the function ( y = 2 + \sin(x) ), we need to determine the possible values of ( y ) for all possible values of ( x ). Since ( \sin(x) ) varies between -1 and 1, the maximum and minimum values of ( y ) occur when ( \sin(x) ) is 1 and -1, respectively.

When ( \sin(x) = 1 ), ( y = 2 + 1 = 3 ). When ( \sin(x) = -1 ), ( y = 2 - 1 = 1 ).

Therefore, the range of the function is ( 1 \leq y \leq 3 ), or in interval notation, ( [1, 3] ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.