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onegirl

  • 2 years ago

Determine the intervals on which f(x) is continuous. f(x) = sqrt( x + 3)

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  1. onegirl
    • 2 years ago
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    @Reaper534

  2. onegirl
    • 2 years ago
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    so should i just plug in the number like 6 then add it with 3 and take the square root of the answer?

  3. onegirl
    • 2 years ago
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    @zepdrix can u help?? me

  4. onegirl
    • 2 years ago
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    @blondie16 can u help?

  5. zepdrix
    • 2 years ago
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    Are you familiar with the graph of \(y=\sqrt x\)? It's a good one to memorize, the basic shape.

  6. onegirl
    • 2 years ago
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    yes

  7. zepdrix
    • 2 years ago
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    |dw:1359680242637:dw|So this is what \(y=\sqrt x\) looks like, yes? Our function that they gave us has a +3 under the square root. That represents a horizontal shift to the `left` 3 units.

  8. onegirl
    • 2 years ago
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    okay

  9. zepdrix
    • 2 years ago
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    |dw:1359680353027:dw|So our function would look like this, shifted over to the left 3 units.

  10. zepdrix
    • 2 years ago
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    I guess we actually don't need the graph to figure this one out... Let's just think about what values we're allowed to plug into a square root.

  11. onegirl
    • 2 years ago
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    okay

  12. zepdrix
    • 2 years ago
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    If you plug in x=-3, \(\large f(-3)=\sqrt{-3+3}\) which equals \(0\) yes? So -3 is fine. Let's try plugging in -4, \(\large f(-4)=\sqrt{-4+3}\) which equals \(\sqrt{-1}\). Uh oh! We can't take the square root of a negative value! :O Remember that from math rules?

  13. onegirl
    • 2 years ago
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    yes i do

  14. zepdrix
    • 2 years ago
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    When you need to determine intervals of continuity, you just need to look for numbers that would cause a problem. Those are places where your function is `not` continuous. So we would NOT include those values in our interval.

  15. onegirl
    • 2 years ago
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    okay

  16. zepdrix
    • 2 years ago
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    It turns out that you can plug in larger and larger values of x in the positive direction and you'll get real solutions for f(x). That just means, none of the positive x values are a problem. It seems that if \(x \lt -3\), it creates a negative value under the square root, which is a problem.

  17. zepdrix
    • 2 years ago
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    So our interval would start from -3 and go up to positive infinity, those are all of the x values we can use.

  18. zepdrix
    • 2 years ago
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    In interval notation we would write it like this,\[\huge [-3,\infty)\] See the square bracket? That's to show that we want to `include` the value -3. If we had done a rounded bracket around the -3, it would mean we start at -3 but don't include the number itself. And also, we always put a rounded bracket on infinity. It's not an actual number so we can't include it.

  19. onegirl
    • 2 years ago
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    okay

  20. onegirl
    • 2 years ago
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    okay got you

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