Find the Domain y=2sin(x)+1

Problem

y=2*sin(x)+1

Solution

1. Identify the type of function. The given equation is a transformation of the basic sine function, ƒ(x)=sin(x)

2. Determine the constraints on the input variable x The sine function is defined for all real numbers, as there are no values of x that result in division by zero or the square root of a negative number.

3. Analyze the transformations. The coefficients 2 and 1 affect the range (vertical stretch and vertical shift), but they do not impose any restrictions on the domain.

4. Conclude that the domain includes all possible real values for x

Final Answer

Domain: *(−∞,∞)

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