# Need Help with Pre Calc Functions!

1. Sep 12, 2006

### 1busykid

Hey I am really confused on Functions, and my teacher does not know how to teach properly.. please help me!

I have couple of problems in book can someone explain to me how i would go about doing them...

Question: Determine whether the equation is a function?

#1: y= x²
#2: y= x³
#3: y= 1/x
#4: y= |x|
#5: y²=4-x²

2. Sep 12, 2006

### Nub

This has to do with graphs right? opening up and down?

3. Sep 12, 2006

### CRGreathouse

A function associates exactly one value (in y) to each value in x. A vertical line through any x value should cross exactly one point.

4. Sep 12, 2006

### bomba923

A function f from A to B (commonly denoted as f:A→B) is a binary relation in which
$$\forall a \in A,\;\exists \, {!} \, f\left( a \right) \in B$$.

With the exception of #5,
every equation you listed is (can be represented as) a function $f:\left\{ {X:x \in X} \right\} \to \left\{ {Y:y \in Y} \right\}$

Last edited: Sep 12, 2006
5. Sep 12, 2006

### gnomedt

In English:

A function turns one number, usually written "x", into another number, usually written "y". For example, y = x is a function. This turns the number x into a number y -- in this case, the number y takes the same value as x. Or the function y=4x turns a number x into a number y which is four times the value of x.

The only conditions on a function is that y has to be one number. y can't be "3,4, or 5", "plus or minus 3", or so on, because those represent more than one number.

It's typical to think about functions only in terms of numbers, but a function doesn't necessarily have anything to do with numbers. Remember, although we usually have x and y stand for numbers, it can really stand for anything at all. (Why not?) x can stand for a person, or a word, or anything. For example, you can have x be a type of car, and have y equal "yes" if the car is blue and "no" if it's not. Because each type of car is either blue or not, this is an example of a function. On the other hand, if you make x be the name of a person and y be x's email address, this cannot be a function, because one person can have two email addresses.

In fancy math words, we say that the function "maps" from a certain set of things, called the domain, to another set of things, the range. The domain can be any set of things at all -- numbers, whole numbers, people, words or cars. Similarly, the range can be any set of things -- pumpkins, forums, prime numbers, dogs, etc. The only condition is that if you give it any element of the domain, the function has to pop out with only one element of the range.

6. Sep 12, 2006

### bomba923

Well, technically, a function maps from the domain to the codomain...

The range of f:A→B is simply $\left\{ {f\left( a \right):a \in A} \right\}$, a subset of the codomain (B).

Last edited: Sep 12, 2006
7. Sep 13, 2006

### Robokapp

In even more plain English every time you see a y= and just x or stuff being done to x on the other side it is a function. If it's y^2 It's almoust never a function...unless it also has a module...

basically how to check is as it's been said above: no x-value can have 2 y values. many x-values can have same y-value. for example a vertical line is not a function but a horisontal line is.

you didn't mean "continuous" functions or "1 to 1" functions, you meant just functions right?

8. Sep 13, 2006

### gnomedt

Yes, but I didn't want to complicate it. Other people have already done that. ;)