Question

Could some one explain Functions (discrete math)

Answer 1

a specific question is much easier to answer

Answer 2

this is a pretty vast topic. in fact almost all of math is about functions

Answer 3

Satellite, just give him the basic definition. (My attempt at not barking orders) :P

Answer 4

lol thanks well im about to leave where im at so i will respond back in an hour or so

Answer 5

really it is not even that easy to define a function. took mathemeticians years to nail down the concept

Answer 6

thanks for the fast response tho ill be back on ina bit (yeah i know)

Answer 7

Okay, I'll try to make a solid attempt at this

Answer 8

y = f(x) means y is a function of x. In other words, whatever value of x you put into the equation, when you evaluate it you'll get a specific y value that is based on the x value you put into it.

For example, in the equation:
y = x + 2

If we input x = 1 into the equation, we get the following:
y = 1 + 2
y = 3

So basically, the point (1,3) is on the graph of y = x+2

If x = 2, then:
y = 2 + 2 = 4

So the point (2,2) is on the graph of y = x+2

If x = 3, then:
y = 3+2 = 5

So the point (3,5) is also on the graph.

In fact, for every unique value of x we put into the equation, we will get a corresponding value for y that is unique and different all previous values of y we found using other values of x.

In this case, we can call the equation y = x+2 a function and replace y with f(x):
f(x) = x+2

By definition, for every value of x, there has to be a corresponding y that is unique to the specific value of x we choose for the function.
By default, linear equations will be functions because every unique x produces a unique x and for every x, there exists one corresponding y.
The set of all x values of a function is the domain.
The set of all y values of a function is range.
The size of the domain will equal the size of the range, meaning both sets will have the same number of elements. For example, if the domain has 5 elements, then the range will also have 5 elements. In any case where this is not true, then that equation is not a function.

Examples of equations that are not functions are vertical lines and circles. They are not functions because for certain values of x, there exist more than one value of y that makes the equation true.

Remember for any equation to be a function, there must be only one unique value of y for any given value of x that is placed into the equation.

For functions, the relationship between x and y will always be one-to-one.

Answer 9

In terms of definitions, what I learned a "function" was defined as is as follows:
"A function is a relation that satisfies the function rule."

In terms that actually say more:

"A function from A to B is a relation \(f \subseteq A\times B\)such that for every \(a \in A\) there exists a unique \(b \in B\) such that \( (a, b) \in f \)"

Basically, a unique output for each input.