What is range of f(x) = 2sin5x +5?

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You need to use the following information with respect to the range of sine function, such that:

`y = sin alpha in [-1,1]`

Considering `alpha = 5x` yields:

`y = sin 5x in [-1,1] => -1 <= sin 5x <= 1`

You need to multiply by 2 such that:

`-2 <= 2sin 5x <= 2`

Adding 5 all over, yields:

`-2 + 5 <= 2sin 5x + 5 <= 2 + 5`

`3 <= 2sin 5x + 5 <= 7 => y in [3,7]`

Hence, evaluating the range of the given function y = 2sin 5x + 5, yields `y in [3,7].`

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