# Piecewise defined function

• Apr 19th 2009, 10:22 PM
Chinnie15
Piecewise defined function
I just read a thread in better ways to get help and thought I would make it easier by asking a specific question at a time as I get help. I don't really understand piecewise defined functions. For example:

Suppose that the function h is defined , for all real numbers, as follows.
h(x)= x if x is not equal to -3
5 if x =-3

I know I would have to plug in and solve for both, and make an x-y chart, but I don't get how to do that in this problem.. It still confuses me. I also need to know how to graph it. Any help would be very much appreciated. :)

Thank you,
Brittney
• Apr 19th 2009, 11:23 PM
Prove It
Quote:

Originally Posted by Chinnie15
I just read a thread in better ways to get help and thought I would make it easier by asking a specific question at a time as I get help. I don't really understand piecewise defined functions. For example:

Suppose that the function h is defined , for all real numbers, as follows.
h(x)= x if x is not equal to -3
5 if x =-3

I know I would have to plug in and solve for both, and make an x-y chart, but I don't get how to do that in this problem.. It still confuses me. I also need to know how to graph it. Any help would be very much appreciated. :)

Thank you,
Brittney

What exactly are you trying to do with this piecewise defined function?
• Apr 19th 2009, 11:24 PM
Chinnie15
Graph h
• Apr 19th 2009, 11:26 PM
Prove It
Quote:

Originally Posted by Chinnie15
Graph it

Just graph the function $\displaystyle h(x) = x$, and then at the point on the graph where $\displaystyle x = -3$, put an open dot (as the function is discontinuous at that point) and, also at $\displaystyle x = -3$ place a closed dot where $\displaystyle h(x) = 5$, since $\displaystyle h(x) = 5$ when $\displaystyle x = -3$.
• Apr 19th 2009, 11:34 PM
Chinnie15
Thanks! I am still lost though.. maybe it's just because it's late and I've been in this too long, but I still don't understand where I'm getting these values from. And how would I graph it? What would y be?
• Apr 20th 2009, 04:53 AM
Piecewise functions
Hello Chinnie15
Quote:

Originally Posted by Chinnie15
What would y be?

$\displaystyle y = h(x) =\left\{\begin{array}{c c}x, & \quad {x\ne -3}\\5, & \quad{x = -3}\\\end{array} \right.\$
Quote:

I still don't understand where I'm getting these values from.
When you sketch the graph any function of $\displaystyle x$, it's up to you to decide what values of $\displaystyle x$ you want to include. The general answer is: any values that will show the general appearance of the graph. So in this case, the important thing is to get it right around $\displaystyle x = -3$. So choose values of $\displaystyle x$ from (say) $\displaystyle -10$ to (say) $\displaystyle +5$.
Quote:

And how would I graph it?
In the way that Prove It has described.

• Apr 20th 2009, 06:19 AM
stapel
Quote:

Originally Posted by Chinnie15
Thanks! I am still lost though.. maybe it's just because it's late and I've been in this too long, but I still don't understand where I'm getting these values from. And how would I graph it? What would y be?

I'm sorry, but I don't understand where you are getting stuck...? You are given y = f(x), and a straight line (namely, y = x) to graph. You have exactly one other thing to do: Draw an open circle (indicating the missing point) on the straight line and a dot (indicating the odd point, (x, y) = (-3, 5)) off to the side of the line.

Please reply with clarification regarding what you have done and at what point you're grinding to a halt. Thank you! :D
• Apr 20th 2009, 11:56 AM
Chinnie15
Nevermind, I get it now. :) I have no idea how I forgot h(x) would be a strait line cutting diagonally right through the origin. Now that I actually remember that it's much easier. So that dot in the upper left would just stay there with no line connecting it?
• Apr 20th 2009, 02:25 PM
Prove It
Quote:

Originally Posted by Chinnie15
Nevermind, I get it now. :) I have no idea how I forgot h(x) would be a strait line cutting diagonally right through the origin. Now that I actually remember that it's much easier. So that dot in the upper left would just stay there with no line connecting it?

Yes