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Math Help - Piecewise defined function

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by Chinnie15 View Post
    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?
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    Graph h
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    Quote Originally Posted by Chinnie15 View Post
    Graph it
    Just graph the function h(x) = x, and then at the point on the graph where x = -3, put an open dot (as the function is discontinuous at that point) and, also at x = -3 place a closed dot where h(x) = 5, since h(x) = 5 when x = -3.
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    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?
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  6. #6
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    Piecewise functions

    Hello Chinnie15
    Quote Originally Posted by Chinnie15 View Post
    What would y be?
    y = h(x) =\left\{\begin{array}{c c}x, & \quad {x\ne -3}\\5, & \quad{x = -3}\\\end{array} \right.\
    I still don't understand where I'm getting these values from.
    When you sketch the graph any function of x, it's up to you to decide what values of 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 x = -3. So choose values of x from (say) -10 to (say) +5.
    And how would I graph it?
    In the way that Prove It has described.

    Grandad
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    Talking

    Quote Originally Posted by Chinnie15 View Post
    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!
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  8. #8
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    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?
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  9. #9
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    Quote Originally Posted by Chinnie15 View Post
    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
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