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Math Help - Finding the range of a function (the answer to this is my holy grail)

  1. #1
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    Finding the range of a function (the answer to this is my holy grail)

    y=f(x) such that domain of f(x) is 1≤x≤5 and range is -2≤y≤6

    Can you find the constant A and D so that the range of Af(x)+D is 0≤y≤1?

    YES. IT SAYS YOU CAN.

    I've tried every combination and recombination of things I can think of. how do I find these constants?
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  2. #2
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    Re: Finding the range of a function (the answer to this is my holy grail)

    Quote Originally Posted by UWstudent View Post
    y=f(x) such that domain of f(x) is 1≤x≤5 and range is -2≤y≤6

    Can you find the constant A and D so that the range of Af(x)+D is 0≤y≤1?

    YES. IT SAYS YOU CAN.

    I've tried every combination and recombination of things I can think of. how do I find these constants?
    Think about it this way. The range of f(x) is $-2 \leq y \leq 6$ and you want to move and squeeze this to fit into $0\leq y \leq 1$

    One way to do this is to move it so that the endpoints of one side coincide, and then to squeeze it so that the other ones do.

    So we'd move f(x) to have range $0\leq y \leq 4$ and then we'd squeeze it to have range $0 \leq y \leq 1$

    We move it by adding D. We squeeze it by multiplying by A.

    Do you think you can find D and A now?
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  3. #3
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    Re: Finding the range of a function (the answer to this is my holy grail)

    I hope this helps.

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