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A function can map each element in the domain to only one element in the codomain or range. A relation is not so restricted.
A simple non-mathematical illustration:
relation: y = biological parent(x)
function: z = biological mother(x)
Leaving aside complications from surrogacy or other exceptional situations, each person has only one natural mother. Siblings may share the same natuarl mother but they are different elements of the domain.
However, for each person, there are two biological parents. The relationship or mapping is said to be one to many, and is therefore not a function.
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When can you say that the graph is function or mere relation?
If a vertical line intersects the graph at more than one point then it is not a function.
Is the relation a function?
Not every relation is a function. But every function is a relation. Function is just a part of relation.
How will you determine if a graph is a function or a mere relation?
You use the "vertical line test". If anywhere you can draw a vertical line that goes through two points of the graph, the relation is not a function; otherwise, it is a function. This is just another way of saying that in a function for every x value (input) there is AT MOST one y value (output).
What is the function of a mere?
To hold water. A mere is a lake.
Is mere relations a function?
No.
When can you say that the graph is function or mere relation?
If a vertical line intersects the graph at more than one point then it is not a function.
Compare and contrast relationship and function?
compare & contrast the similarities & differences of a relation & function
What is a mere relation?
A relation is an expression that is not a function. A function is defined as only having one domain per range, meaning that when graphed, a function will have no two points on the same vertical line. If your expression is graphed and two points do appear on the same vertical line, it is a relation, not a function.
How do you identify if an equation is function or mere relation?
you will know if it is Function because if you see unlike abscissa in an equation or ordered pair, and you will determine if it is a mere relation because the the equation or ordered pairs has the same abscissa. example of function: {(-1.5) (0,5) (1,5) (2,5)} you will see all the ordinates are the same but the abscissa are obviously unlike example of mere relation: {(3,2) (3,3) (3,4) (3,5)} you will see that the ordinates aren't the same but the abscissa are obviously the same. Try to graph it.!
Is the relation a function?
Not every relation is a function. But every function is a relation. Function is just a part of relation.
How will you determine if a graph is a function or a mere relation?
You use the "vertical line test". If anywhere you can draw a vertical line that goes through two points of the graph, the relation is not a function; otherwise, it is a function. This is just another way of saying that in a function for every x value (input) there is AT MOST one y value (output).
What is the function of a mere?
To hold water. A mere is a lake.
How can you determine that a set of ordered pairs are a graph table diagram equation a function or mere relation?
In general you cannot. Any set of ordered pairs can be a graph, a table, a diagram or relation. Any set of ordered pairs that is one-to-one or many-to-one can be an equation, function.
Can you have a function that is not a relation?
No, a function must be a relation although a relation need not be a functions.
Is mere relations a function?
No.
Which of these data sets represents a function?
Does the graph above show a relation, a function, both a relation and a function, or neither a relation nor a function?
Is a function always a relation and a relation always a function?
yes.
