The term “quotient function” can refer to a few different things:

**Quotient Functions (a type of function in calculus)**- Definition,
- Domain,
- Quotient of Two Functions Example.

- The
**Quotient Function in Excel**

**See also:**

What is the Difference Quotient?

What is the Quotient Rule?

## 1. Quotient Function (Type)

## A. Definition

A **quotient function **is a type of function where two functions are separated by a division sign. For example:

- f(x)/g(x)
- X
^{2}/x

## B. Domain of a Quotient of Two Functions

The quotient of two functions, f(x) and g(x), has a domain A ∩ B (“A intersected with B” means *the set of all points that A and B have in common*), excluding where g(x) = 0.

The quotient is given by the following formula:

**Example question:** If f(x) = √ (x + 1) and g(x) = 2x + 1:

- What is the quotient(q) of f and g?
- What is the domain of q?

**Solution**:

Part 1: Plug the given functions into the formula:

Part 2: Find the domains for the two separate functions. As noted above, the denominator (in this case, 2x + 1) can’t equal zero. In other words, x ≠ -½.

The domain is all points that the two functions have in common.

- The domain of f(x) = √(x + 1) is A = [-1, ∞).
*Why*? Any number above -1 is fine, but -1 itself would give a denominator of 0. Any number lower than that, and you would be finding the square root of a negative number. - The domain of g(x) = B = (-∞, ∞).

The domain of the two functions overlap at [-1, ∞], so that’s the domain of this particular quotient function.

## 2. Quotient Function in Excel

The format for this function is:

QUOTIENT(numerator, denominator)

**Note**: A “function” in Excel refers to a predefined formula that performs calculations.

The quotient function in Excel is a bit of an oddity, because it only returns integers. For example, =QUOTIENT(7,2) gives a solution of 3 because QUOTIENT doesn’t give remainders. In other words, you should only use it if you want to discard a remainder. If you wanted to do a straightforward division (with remainder), just use the forward slash. For this example, type =7/3 into a cell instead.

## References

Microsoft Office. Quotient Function. Retrieved October 19, 2019 from: https://support.office.com/en-us/article/quotient-function-9f7bf099-2a18-4282-8fa4-65290cc99dee

Tan S. (2008). Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach. Cengage Learning.

Wilson, R. (2013). Much Ado About Calculus: A Modern Treatment with Applications Prepared for Use with the Computer. Springer Science and Business Media. Retrieved OCtober 16, 2019 from: https://books.google.com/books?id=mqQACAAAQBAJ

**CITE THIS AS:**

**Stephanie Glen**. "Quotient Function: Definition, Excel, Domain" From

**CalculusHowTo.com**: Calculus for the rest of us! https://www.calculushowto.com/quotient-function/

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