defining functions

[dalopez]

Defining functions are simple when the equation is simple such as y = x + 2 because all variables plug in to a graph. But how do you solve for harder question like this?

f(x) = 2 if x>1
f(x) = -1 otherwise

 

[tkhunny]

One way is simply to define them both as if they existed over the entire domain. Then just ignore tha parts you don't want. It can get a little messy.

Your calculator may also have logical structures that allow you to restrict the Domain. I have not seen very many of these, but I don't play with graphing calculators all that much so I may be entirely wrong.

 

[stapel]

Defining functions are simple when the equation is simple such as y = x + 2 because all variables plug in to a graph. But how do you solve for harder question like [piecewise functions]?

What do you mean by "defining" the function? (Since the "f(x)=" part is the "definition" of the function, you must mean something other than "defining what the function is", is why I ask.)

Also, what do you mean by "solving for harder questions"? (There is no "question" (instructions, exercise, thing to do, etc) in your example, and nothing to "solve" for, is why I ask.)

Please be specific. It would probably help if you posted the complete text of and instructions for the exercise with which you are having difficulty.

Thank you!

Eliz.

 

[dalopez]

Seems I was too vaque on my last post. Remember I am confused. The question I am being asked in class is "is the equation a function?" One problem given is

1. f(x) = 2 if x>1
f(x) = -1 otherwise

How do I find out if this is a function? What are the rules to follow? I understand the vertical line test, but where to I get the x,y coordinates to plug in to a graph to actually use the vertical line test. I also understand that for every x there can only be one y. I hope this clarifies my confusion.

 

[stapel]

A function is, among other things, a rule into which you can plug a value (usually "x") and get one (and only one) output value (usually "y" or "f(x)").

So look at the relation they defined for you. If you pick an x and plug it in, how many y-values do you get for that x? So is the relation a function, or not? :wink:

Eliz.

 

[pka]

1. f(x) = 2 if x>1
f(x) = -1 otherwise
How do I find out if this is a function? What are the rules to follow?

I sympathy for you: current mathematics education has failed you.
Trying to dumb-down the definition of function has lead to your confusion!

Proper definition of a function.
A function is a set of ordered pairs having the property that not two pairs have the same first term. The domain of a function is simply the set of first terms of the pairs in the function. And if f is a function from a set A to set B then each x in A is the first term of some pair in f.

Forget the vertical line test.
Ask yourself; using the given definition can two ordered have the same first term?
If the answer is no, then it is a function!