# Piecewise function

• May 9th 2013, 11:45 AM
Oldspice1212
Piecewise function
Hey I'm not to sure how to set it up on here, but I'll try my best to make sense of the question,

f(x) = { 3-1/2x if x is less than = 2, 2x-5 if x greater than 2

So I have to find the domain and sketch the graph, this is what I have;

I first thought I was suppose to make 3-1/2x = 0 and isolate x for domain, but I think for these piecewise functions I just plug in the 2 and see what the function equals to and I can get the domain?

f(2) = 3-1/2(2) = 2
f(2) = 2(2)-5 = -1

So the domain is ( - infinity, 2]U(-1, infinity)?

And the graph I believe would be two likes going down first and fourth quadrant, this kind of looks odd to me and I'm not sure what I really did wrong? Thanks.
• May 9th 2013, 11:56 AM
HallsofIvy
Re: Piecewise function
Surely you know that "f(x)= 0" has nothing at all to do with the domain? And the value of f(2) (or the limit as x approaches 2 from above) has nothing to do with the domain. The domain is a matter of values of x, not values of f(x).

You are are told what f(x) is for all x less than or equal to 2 and for all x greater than 2. That covers all possible values of x doesn't it?
Are you clear on what "domain" means?
• May 9th 2013, 12:23 PM
Oldspice1212
Re: Piecewise function
Quote:

You are are told what f(x) is for all x less than or equal to 2 and for all x greater than 2. That covers all possible values of x doesn't it?
Are you clear on what "domain" means?
Not in this question lol, but its the set of all inputs of x or something.
• May 9th 2013, 02:31 PM
Oldspice1212
Re: Piecewise function
Ok so isn't the domain all real numbers since it shows x is less than = 2 and x is greater than 2 so that means it's all real numbers right?
• May 9th 2013, 03:25 PM
HallsofIvy
Re: Piecewise function
Yes, the domain is the set of all real numbers.
• May 9th 2013, 03:45 PM
Plato
Re: Piecewise function
Quote:

Originally Posted by Oldspice1212
Ok so isn't the domain all real numbers since it shows x is less than = 2 and x is greater than 2 so that means it's all real numbers right?

You seem to be too lazy to do any preparation for this question.
You need to know what domain means. But make on effort to learn.

You have made no effort to type the question in a readable format.

It maybe $f(x)=\begin{cases}3-\dfrac{1}{2x} &:\; x\le2\\2x-5 &:\; x>2\end{cases}$

Now if I have made a correct guess at the mess you posted, then clearly $x\ne 0$ because the function is not defined at $x=0$.
• May 9th 2013, 03:48 PM
HallsofIvy
Re: Piecewise function
Oops, right. 0 is included in $x\le 2$ but $3- \frac{1}{2x}$ is not defined at x= 0.
• May 9th 2013, 04:18 PM
Plato
Re: Piecewise function
Quote:

Originally Posted by HallsofIvy
Oops, right. 0 is included in $x\le 2$ but $3- \frac{1}{2x}$ is not defined at x= 0.

Well yes, but the point is: what does the OP mean?

It may no be that at all!
• May 9th 2013, 07:18 PM
Oldspice1212
Re: Piecewise function
Quote:

You seem to be too lazy to do any preparation for this question.
You need to know what domain means. But make on effort to learn.

You have made no effort to type the question in a readable format.

It maybe

Now if I have made a correct guess at the mess you posted, then clearly because the function is not defined at .
Pretty quick judgement, I actually have no clue how to make it fancy like that, so sorry.

0 is included from what I can tell, and the domain of the function is a set of all real numbers (don't make it complicated :P). I was confusing myself earlier but I figured it out eventually, and I also made the graph, but thank you for the help guys.
• May 9th 2013, 09:25 PM
Prove It
Re: Piecewise function
I suggest you read what Plato wrote out in post 6, and advise us whether the function he wrote is correct. If it is, then you have made a mistake and you need to take in what Plato and HallsofIvy have been trying to tell you about the domain of this particular function, because it would NOT be all the reals!
• May 10th 2013, 03:04 PM
Oldspice1212
Re: Piecewise function
Oh crap, the 1/2x forgot about that it can't be 0, and I already handed the assignment in...gah
• May 10th 2013, 03:27 PM
Plato
Re: Piecewise function
Quote:

Originally Posted by Oldspice1212
the 1/2x forgot about that it can't be 0, and I already handed the assignment in...gah

You have still missed my point completely

You posted 1/2x that is read as $\frac{1}{2}~x$.

It appears that you actually mean $\frac{1}{2x}$ in which case use grouping symbols: 1/(2x).
• May 10th 2013, 03:36 PM
Oldspice1212
Re: Piecewise function
Quote:

You have still missed my point completely

You posted 1/2x that is read as .

It appears that you actually mean in which case use grouping symbols: 1/(2x).
Yes I did mean that, because I looked at the piece wise you set up 1/(2x) but I just saw the actual question was 1/2x so I think it still stands at being the set of all real numbers, I don't see it being anything else.