# What is the domain and range of a sine graph?

##### 2 Answers

Let

Where

#A = "Amplitude"# #2pi//B = "Period"# #-C//B = "Phase shift"# #D = "Vertical shift"#

The maximum domain of a function is given by all the values in which it is well defined:

Since the sine function is defined everywhere on the real numbers, its set is

As

Hence:

The range depends on the sign of

then the range is more simply defined as *[D-A, A+D]*.

As a conclusion,

**Domain**:

**Interval Notation:**

**Range**:

**Interval Notation:**

#### Explanation:

**Domain and Range of a SIN Graph**:

Let us look at the SIN Graph first:

The **domain** of a function is the **set of input values** for which the function is **real and defined**.

**Domain restriction** used for the SIN Graph to display ONE complete cycle.

The set of output values (of the dependent variable) for which the function is defined.

As you can easily observe, the SIN graph goes up until

Hope this helps.