Evaluating A Step Function

Discussion in 'Other Pre-University Math' started by nycmathguy, Jul 20, 2021.

  1. nycmathguy

    nycmathguy

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    The following examples are not from my textbooks.

    I understand that for f(x) = [[ x ]], we round down if x is not an integer. I also know that f(x) is less than or equal to x.

    Sample:

    Evaluate g(x) = 3[[ x ]] for x = 2, x = 0.6, and x = -4.

    Let x = 2

    I know that 2 is an integer.

    So, g(2) = 3[[ 2 ]] becomes 3(2) = 6.

    Let x = 0.6

    I know that 0.6 is not an integer. So, I must round down.

    Number Line

    <------(0)--------(0.6)---------(1)-------->

    If I round down, the closes number on the line is 0.

    So, g(0) = 3[[ 0 ]] = 3(0) = 0.

    Let x = -4

    I know that -4 is an integer. No need to round down.

    So, g(-4) = 3[[ -4 ]] becomes 3(-4) = -12.

    You say?
     
    nycmathguy, Jul 20, 2021
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  2. nycmathguy

    MathLover1

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    perfect!
     
    MathLover1, Jul 22, 2021
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    nycmathguy likes this.
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  3. nycmathguy

    nycmathguy

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    I am going to finish this week evaluating step functions. There are 2 more questions with 4 parts that will be posted with work shown.
     
    nycmathguy, Jul 22, 2021
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