Functions

[wiseone]

I really don't know what a function is and I need to get a good definition of it. Also can someone tell me what this means.

A function is something like f(x)=2x-3

What you do is plug in a given number for x

For example, for the previous question above they might say next to it:
solve for f(5)=2x-3

That means to plug in 5 for x

Your answer would b3 f(5)=7

 

[CodePoet]

A function, written f(x) (read as "f of x") equal to an algebraic expression means that for any number x, you get one answer out. In your example
f(x)=2x-3, that means whatever you are told equals x, gets placed into the algebraic expression.
f(5)=2x-3 <---here you're being told to put 5 as x, that means you replace all x in the expression with 5
f(5)=2(5)-3
f(5)=10-3
f(5)=7
I'm not sure if this helps you or not as the line "A function is something like f(x)=2x-3" is a pretty basic explanation of what a function is. It's different than y=2x-3 because you're not being explicitly told what to put as x as in f(5)=2x-3.

 

[mmm4444bot]

I really don't know what a function is, and I need to get a good definition of it …

Hello Wise One!

I'm glad to learn that you think it's important to have a good understanding of "functions". I think it's very important, too, for anyone who intends to prepare for college.

I'm not a classroom teacher, but, if I were, I would anticipate needing at least three 50-minute class periods to adequately explain both the concept of function and the notations we use to express it. I would use many visual aids.

(I wish it were simple to produce such an explanation here, but it's not.)

Do you have a textbook? If so, is there anything in the text's definition or examples that's not clear for you? We can take care of that here, if you post specific questions.

Otherwise, there's a wealth of information about functions, on the Internet. Use Google to search on keywords: what is a function in math.

Many of the resulting sites will not make sense to you, so skip those and move on to others. You need to invest a few hours reading and thinking. If you check out sufficient sites, then you'll eventually find pieces of information that make sense, to you. As you practice with more applications and exercises, these pieces will start to come together, and you'll eventually have a good understanding.

Again, we're here to help with specific questions, so feel free to post as many as you like.

Basically, a function is a relationship between two sets of numbers, where the numbers in one set (called the range) DEPEND UPON the numbers in another set (called the domain).

Simple examples: a person's height depends upon their age; the strength of a planet's gravity depends upon its size; the price you pay for a sack of rice depends upon its weight.

There are at least four different ways to define (i.e., identify or state) functional relationships.

Algebraic: Many functions can be defined by some sort of formula.

Numerical: Functional relationships can be defined by a table (i.e., listing the corresponding numbers in the domain and range).

Graphical: Functions can be defined by a picture (eg: scatter plot, bar-chart, graph)

Descriptive: Some functions can only be defined in words.

'

… the line "A function is something like f(x)=2x-3" is a pretty basic explanation of what a function is. It's different than y=2x-3 …

Hi, Code Poet. This difference is one of notation only.

The equation y = 2x - 3 defines a functional relationship between y and x.

Writing f(x) = 2x - 3 defines the same function. Function notation uses the symbol "f(x)" to represent the dependent variable, instead of the symbol "y".

But, you're right, if you're thinking that function notation shows us additional information.

For example, in this linear function, I could write either of the following.

y = 17

f(10) = 17

In the first statement, we know that 17 is in the range of the function, but we don't explicity see which value of x (from the domain) produces it.

In the second statement (using function notation for y), we explicitly see that it's the number 10 from the domain that corresponds to the number 17 in the range.

(Also, with this notation, we've given the function a name: f. It's essential to name individual functions, when we discuss multiple functions at once; otherwise, we'd have no way of knowing to which particular function the symbol y belongs.)

Function notation also shows that f(10) represents a CONSTANT, whereas f(x) represents a VARIABLE.

Cheers ~ Mark

 

[wiseone]

A function, written f(x) (read as "f of x") equal to an algebraic expression means that for any number x, you get one answer out. In your example
f(x)=2x-3, that means whatever you are told equals x, gets placed into the algebraic expression.
f(5)=2x-3 <---here you're being told to put 5 as x, that means you replace all x in the expression with 5
f(5)=2(5)-3
f(5)=10-3
f(5)=7
I'm not sure if this helps you or not as the line "A function is something like f(x)=2x-3" is a pretty basic explanation of what a function is. It's different than y=2x-3 because you're not being explicitly told what to put as x as in f(5)=2x-3.

But how do you get 5. I went on this site http://www.coolmath.com/algebra/Algebra1/14Functions/01_whatarethey.htm

And it was pretty good but still got confusing.

 

[Aladdin]

But how do you get 5. I went on this site http://www.coolmath.com/algebra/Algebra ... rethey.htm

And it was pretty good but still got confusing.

I was surprised that you didn't respond to Mark's reply or the important informations he gave , I think it helped a lot .

 

[mmm4444bot]

But how do you get 5 …

… [coolmath.com] was pretty good but still got confusing.

If they asked you to find the value of the constant f(5), then the 5 is given to you.

Is that the 5 you're asking about ?

And, what did you find confusing about function descriptions at coolmath.com ?

We can help you, if you can ask specific questions.