What is the domain and range for the equation y=1+2sinx𝑦=1+2sin𝑥?
Question
What is the domain and range for the equation y=1+2sinx𝑦=1+2sin𝑥?
Solution
The domain and range of a function are the set of all possible input values (x-values) and output values (y-values), respectively.
For the function y = 1 + 2sinx:
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Domain: The domain of the sine function is all real numbers, because the sine function is defined for any real-numbered input. Therefore, the domain of y = 1 + 2sinx is all real numbers, or (-∞, ∞).
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Range: The range of the basic sine function is [-1, 1]. Since the function y = 1 + 2sinx includes a vertical stretch by a factor of 2 and a vertical shift upward by 1 unit, the range will be [1 - 2, 1 + 2] or [-1, 3].
So, the domain of the function y = 1 + 2sinx is (-∞, ∞) and the range is [-1, 3].
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