Table of Contents
- 1 What is a relation that assigns exactly one output value to one input value?
- 2 What is a relation that assigns exactly one value in the range to each value of the domain?
- 3 What is the relationship between a relation and a function?
- 4 What is a relation for each value of the first component of the ordered pairs there is exactly one value of the second component?
- 5 How do you identify a one-to-one function?
- 6 Can each input have the same output?
What is a relation that assigns exactly one output value to one input value?
Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
What is a relation that assigns exactly one value in the range to each value of the domain?
A function f is a relation that assigns a single value in the range to each value in the domain. In other words, no x-values are repeated.
What is special type of relation that pairs each domain value with exactly one range value?
function
A function is a special type of relation where every input has a unique output. Definition: A function is a correspondence between two sets (called the domain and the range) such that to each element of the domain, there is assigned exactly one element of the range.
What is the relationship between a relation and a function?
Ans: A relation represents the relationship between the input and output elements of two sets whereas a function represents just one output for each input of two given sets.
What is a relation for each value of the first component of the ordered pairs there is exactly one value of the second component?
A very important type of relation called a function. A function is a set of ordered pairs in which each first component corresponds to exactly one second component.
What do you call a relation where each in the domain is related to only one value in the range by some rules?
A relation in which each element in the domain corresponds to exactly one element in the range is a function. A function is a correspondence between two sets where each element in the first set, called the domain, corresponds to exactly one element in the second set, called the range.
How do you identify a one-to-one function?
An easy way to determine whether a function is a one-to-one function is to use the horizontal line test on the graph of the function. To do this, draw horizontal lines through the graph. If any horizontal line intersects the graph more than once, then the graph does not represent a one-to-one function.
Can each input have the same output?
Each input has only one output, and the fact that it is the same output (4) does not matter. This relation is a function. Remember that in a function, the input value must have one and only one value for the output.