Question

What are the similarities and differences between a relation and a function?

Answer 1

a function is when one x value has one y value, a relation is when u basically have a table

Answer 2

Okay cool what are the similarities

Answer 3

that a function is a relation, but a relation is not a function

Answer 4

I have the definitions of them from my Algebra Textbook if you want them.

Answer 5

Best AnswerAsker's Choice

dogwood_lock answered 7 years ago

A function is a special kind of relation. Relations pair up x and y coordinates, either by listing them (explicitly) or by writing an equation (implicitly). Functions have the additional property that no two values of y have the same value of x.

Put another way, if you view x as the input and y as the output, functions have the property that each input yields only one output. If you ever see the situation where a single input has two different outputs, that is not a function.

If the relation is stated explicitly, look at the (x,y) pairs and see if you can find two of them which have the same x but different y's. If you can, then it's NOT a function. If you can't, then it IS a function.

If the relation is given as an equation, look for certain clues that will tell you that it's not a function. If the equation has a y-squared in it (or y raised to the power of any even number) then it's NOT a function. If there's a plus/minus sign in the equation, it probably is NOT a function. If there are absolute value signs in the equation, and there's a y inside the signs, then it probably is NOT a function.

Another way to tell is to graph the relation and look for places where a single x value has two different y values. This is called the vertical line test. If there is a place where a vertical line would touch the relation in two different places, then it's NOT a function, It's just a relation.

Examples:

y = 3 + x is both a relation and a function.
x + y^2 = 10 is a relation but not a function.
{(3,2),(4,5),(3,6)} is a relation but not a function.

Answer 6

That would be good to @mipie13 thanks and thank you @jzellem1004

Answer 7

All linear equations of the form y = mx + b, where m and b are real-valued constants, are functions.

A linear equation of the form x = a, where a is a constant is not a function.

Functions must be one-to-one. That means each x-value is paired with exactly one y-value.

Answer 8

Function- A relation that assigns to each member of the domain exactly one member of the range.
Relation- Any set of ordered pairs.
(From my textbook.) :)

Answer 9

Thank you everyone so much!!!

Answer 10

You're welcome! :)