## How do you know if the relation is a function?

Identify the input values. Identify the output values. **If** each input value leads to only one output value, classify the **relationship** as a **function**. **If** any input value leads to two or more outputs, do not classify the **relationship** as a **function**.

## What is a relation that is a function?

A **function** is a **relation** in which each input has only one output. In the **relation**, y is a **function** of x, because for each input x (1, 2, 3, or 0), there is only one output y. x is not a **function** of y, because the input y = 3 has multiple outputs: x = 1 and x = 2.

## Is a relation always a function?

All **functions** are **relations**, but not all **relations** are **functions**. A **function is a relation** that for each input, there is only one output. Here are mappings of **functions**. The domain is the input or the x-value, and the range is the output, or the y-value.

## How do you know if a relation is not a function?

ANSWER: Sample answer: You can **determine whether** each element of the domain is paired with exactly one element of the range. For example, **if** given a graph, you could use the vertical line test; **if** a vertical line intersects the graph more than once, then the **relation** that the graph represents is **not a function**.

## What is the difference between a relation and function?

A **relation** is any set of ordered pairs. A **function** is a set of ordered pairs where there is only one value of begin{align*}yend{align*} for every value of begin{align*}xend{align*}.

## Whats a function and not a function?

A **function** is a relation between domain and range such that each value in the domain corresponds to only one value in the range. Relations that are **not functions** violate this definition. They feature at least one value in the domain that corresponds to two or more values in the range. Example 4-1.

## What is relation with example?

A **relation** between two sets is a collection of ordered pairs containing one object from each set. If the object x is from the first set and the object y is from the second set, then the objects are said to be related if the ordered pair (x,y) is in the **relation**. A function is a type of **relation**.

## Is a circle a function?

No. The mathematical formula used to describe a circle is an equation, not one function. For a given set of inputs a function must have at most one **output**. A circle can be described with two functions, one for the upper half and one for the lower half.

## Is a one to many relation a function?

The y-side has either two lines going to it or **one**. So, the y side is **many**. This **relation** is **one-to-many**, which is a **function**!

## Why is every relation not a function?

However, **not every relation** is a **function**. In a **function**, there cannot be two lists that disagree on only the last element. This would be tantamount to the **function** having two values for one combination of arguments. By contrast, in a **relation**, there can be any number of lists that agree on **all** but the last element.

## How do you know if a function is not a function?

Determining whether a relation is a **function** on a graph is relatively easy by using the vertical line test. If a vertical line crosses the relation on the graph only once in all locations, the relation is a **function**. However, if a vertical line crosses the relation more than once, the relation is **not** a **function**.

## How do you tell if a graph represents a function?

Use the vertical line test to **determine whether** or not a **graph represents a function**. **If** a vertical line **is** moved across the **graph** and, at any time, touches the **graph** at only one point, then the **graph is a function**. **If** the vertical line touches the **graph** at more than one point, then the **graph is** not a **function**.

## What is the domain in a function?

**Functions** assign outputs to inputs. The **domain** of a **function** is the set of all possible inputs for the **function**. For example, the **domain** of f(x)=x² is all real numbers, and the **domain** of g(x)=1/x is all real numbers except for x=0. We can also define special **functions** whose **domains** are more limited.