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Math Help - Please help me find the piecewise equation

  1. #1
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    Please help me find the piecewise equation

    Please help me find the formula for b). I have tried everything already and it is driving me nuts trying to find a formula for this problem.

    So far I have this f(x) = { 1 x > 1
    {1 + x

    f(x) = { 1 x > 1
    {(10)(x) + x

    I understand that the problem is asking for the formula but what I don't get is how to write a formula for it. Every problem is different so how as I suppose to write a general formula for it. Such as if the difference is .99 the maximum the customer would get back is 5 dollars + .99. So that wouldn't be the same for if the difference was .10. Please help me with this.

    Thanks.

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  2. #2
    MHF Contributor ebaines's Avatar
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    I am going to assume that the rules for the refund are this -- for an over-charge of $x:

    1. Customer gets a min of $1 + x
    2. If the overage is between $0.10 and $0.50, the customer gets a rebate of 10 times the overage plus the overage, for a total of 11 times x.
    3. If the overage is $0.50 or more, then the custmer gets $5 plus x.

    If this is correct, then you have:

    <br />
y = \left \{\begin{matrix} {\$1+x} & {for\ \$0.00 \leq x \leq \$0.10}\\{11x}&{for \ \$0.10 \leq x \leq \$0.50}\\{\$5 + x}&{for \ \$0.50 \leq x}\end{matrix} \right.<br />
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