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Math Help - simple function question

  1. #1
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    simple function question

    how many of the following are functions?

    y= 2x+7
    y= √(5-x) (all under the rad)
    y= 1/(x+62) - 2
    y= -3^x + 41 (no parentheses around the -3 purposely)

    i think they all are?
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  2. #2
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    Re: simple function question

    The top equation doesn't look like a function. It has two outputs for one input.

    f(x) = y= 2x+7
    Example: f(2) = 2(2)+7 = 11 and 3.

    Graph it. It won't pass the vertical line test. A vertical line can pass through two points.
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  3. #3
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    Re: simple function question

    Quote Originally Posted by IdentityProblem View Post
    The top equation doesn't look like a function. It has two outputs for one input.

    f(x) = y= 2x+7
    Example: f(2) = 2(2)+7 = 11 and 3.

    Graph it. It won't pass the vertical line test. A vertical line can pass through two points.
    thanks ill try that. how can i algebraically check for the other ones?
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  4. #4
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    Re: simple function question

    Hell0,

    1. What is the definition of a function?
    2. What are some tests you can apply to check whether a relation is a function?
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  5. #5
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    Re: simple function question

    Quote Originally Posted by phys251 View Post
    Hell0,

    1. What is the definition of a function?
    2. What are some tests you can apply to check whether a relation is a function?
    haha I can graph it I know. but the pictures aren't so clear and I'm not good at changing the view
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  6. #6
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    Re: simple function question

    ok so the first one is not. and the second one is not also. not sure about the bottom two
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  7. #7
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    Re: simple function question

    Quote Originally Posted by Hell0 View Post
    thanks ill try that. how can i algebraically check for the other ones?
    You can substitute in an arbitrary variable like a into the equation as the "input."
    This will lead to some "output."

    A function can only have one unique output for every input; otherwise, it is not a function.

    For example:
    f(x) = y= 2x+7
    f(a) = 2(a)+7 = -2a+7 and 2a+7. Those are two different outputs for that one input; hence, it is not a function.

    For example:
    f(x) = y= √(5-x)
    f(a) = √(5-a) This leads to only one result; hence, it passes the test. This is a function. An input only gives one output.

    -----

    Another example:
    x2 + y2 = 1
    Is that a function?
    Algebraically, we can rewrite it by solving for y.
    y2 = -x2 + 1
    √(y2) = √(-x2 + 1)
    y = √(-x2 + 1)
    This is not a function. The tells us that there will be two outputs for a single input.

    Again, you can put a in to make sure. y = √(-(a)2 + 1) = +√(-(a)2 + 1) and -√(-(a)2 + 1)
    Last edited by IdentityProblem; September 2nd 2013 at 05:00 PM.
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  8. #8
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    Re: simple function question

    wow. and I got a 99 on the a2/trig regents last year. I'm embarrassed. I'll write back when I have an answer for the other two
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  9. #9
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    Re: simple function question

    1. no
    2. yes
    3. yes
    4. yes

    how did i do
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