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Shido88

  • 3 years ago

Graph piecewise function: p(x)={1/2x+1 if x cannot equal to 4 {2 if x = 4 State Domain and Range

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  1. zepdrix
    • 3 years ago
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    |dw:1359425377274:dw|Basically what we want to do is - think of this as two different functions. It's the function \(p(x)=\dfrac{1}{2}x+1\) when `x is not 4`. And it's a different function \(q(x)=2\) when `x is 4`. So let's graph what I called `q` first, since that one is easy. c:

  2. Shido88
    • 3 years ago
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    ok :)

  3. Shido88
    • 3 years ago
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    so when x is not 4, that mean i can select x to be any number just dont pick 4 right ?

  4. zepdrix
    • 3 years ago
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    For all values of x, the function produces `2`. Normally that would look like a horizontal line like this,|dw:1359425605017:dw|But this function is only defined at x=4! So what we actually get is this.|dw:1359425634168:dw|

  5. zepdrix
    • 3 years ago
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    Oh sorry I was looking at the `x is 4` one first c: heh

  6. Shido88
    • 3 years ago
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    oh

  7. zepdrix
    • 3 years ago
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    I should delete that line on x=4.. I think that's confusing maybe.

  8. Shido88
    • 3 years ago
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    plz keep explaining...i got emergency but i brb thanks! :]

  9. zepdrix
    • 3 years ago
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    k

  10. zepdrix
    • 3 years ago
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    When `x is not 4` we have a linear function. It has a slope of 1/2, and a y-intercept of 1.

  11. zepdrix
    • 3 years ago
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    So it will cross the y-axis at y=1

  12. zepdrix
    • 3 years ago
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    |dw:1359425801166:dw|Remember, we can only graph this line where `x is not 4`. So when we get to that spot where x is 4, we draw an open circle to show that the line is not defined there.

  13. zepdrix
    • 3 years ago
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    The black dots on the left don't actually mean anything. I was just plotting a couple points so I could draw a line through them.

  14. Shido88
    • 3 years ago
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    @zepdrix what about the green dot ?

  15. Shido88
    • 3 years ago
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    so when x cannot equal to 4 then just don't include the 4

  16. Shido88
    • 3 years ago
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    oh i see now, the green dot is x=4 and it just a linear line

  17. zepdrix
    • 3 years ago
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    Yah the green dot is where the function is defined when `x=4`. It's like you have a straight line, with a hole in it at one spot. Think of a straight line, and one of the points broke off the line and fell to a spot below somewhere. The function is still defined at x=4, just in a different place, not along the line where you would normally think. Sorry late response :C site being slow tonight.

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