Find the domain and the range of the function `y=f(x)`, where `f(x)` is given by
`sinx`

Answer

To find the domain and range of the function \( y = f(x) \), where \( f(x) = \sin x \), we can follow these steps:

### Step 1: Determine the Domain
The domain of a function is the set of all possible input values (x-values) for which the function is defined.

- The sine function, \( \sin x \), is defined for all real numbers. This means that you can input any real number into the sine function, and it will produce a valid output.

**Domain:**
\[ \text{Domain of } f(x) = \sin x \text{ is } (-\infty, \infty) \]

### Step 2: Determine the Range
The range of a function is the set of all possible output values (y-values) that the function can produce.

- The sine function oscillates between -1 and 1. This means that the maximum value of \( \sin x \) is 1, and the minimum value is -1. Therefore, the output of the sine function will always lie within this interval.

**Range:**
\[ \text{Range of } f(x) = \sin x \text{ is } [-1, 1] \]

### Final Answer
- **Domain:** \( (-\infty, \infty) \)
- **Range:** \( [-1, 1] \)

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