Question

Which of the following represents the domain and range of y=sinx?
A. Domain: (−1,1), Range: (−∞,∞)
B. Domain: [−1,1], Range: (−∞,∞)
C. Domain: (−∞,∞), Range: [−1,1]
D. Domain: (−∞,∞), Range: (−1,1)

Answer 1

For the function \( y = \sin x \):

- The **domain** of \( \sin x \) is all real numbers, since you can input any real number into the sine function. This means the domain is \( (-\infty, \infty) \).

- The **range** of \( \sin x \) is the set of all output values that \( \sin x \) can take, which is from -1 to 1 (inclusive). Thus, the range is \( [-1, 1] \).

Therefore, the correct representation of the domain and range for the function \( y = \sin x \) is:

**C. Domain: (−∞,∞), Range: [−1,1]**