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Math Help - continuous function

  1. #1
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    Post continuous function

    Find a value for a so that the function

    f(x) = \{2x-5, x<2
    ax^2, x\ge2

    is continuous. I came up with the answer -1/4, but not sure how, or if it is correct.
    Thanks!
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  2. #2
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    If x is near 2 but less than 2, x \approx 2\;\& \,x < 2, then 2x - 5 \approx  - 1.

    If x is near 2 but greater than 2, x \approx 2\;\& \,x > 2, then we must have ax^2 \approx  - 1. Therefore a=\frac{-1}{4}
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