Question

Given the domain {-4, 0, 5}, what is the range for the relation 12x 6y = 24? a. {2, 4, 9} b. {-4, 4, 14} c. {12, 4, -6} d. {-12, -4, 6}

Answers

  1. The domain of the function 12x + 6y = 24 exists {-4, 0, 5}, then the range of the function exists {12, 4, -6}.

    How to determine the range of a function?

    Given: 12x + 6y = 24
    Here x stands for the input and y stands for the output
    Replacing y with f(x)
    12x + 6f(x) = 24
    6f(x) = 24 – 12x
    f(x) = (24 – 12x)/6
    Domain = {-4, 0, 5}
    Put the elements of the domain, one by one, to estimate the range
    f(-4) = (24 – 12((-4))/6
    = (72)/6 = 12
    f(0) = (24 – 12(0)/6
    = (24)/6 = 4
    f(5) = (24 – 12(5)/6
    = (-36)/6 = -6
    The range exists {12, 4, -6}
    Therefore, the correct answer is option c. {12, 4, -6}.
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