what is the domain and range of (f)?

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  • 3 weeks ago
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    The DOMAIN of a function is all possible INPUT (x) values.

    Start scanning the function going left to right.

    The leftmost value is x = -1 (with a solid dot)

    The rightmost value is x = 3 (with a solid dot)

    And there is a value for every x in between (notice that part of the graph has a solid dot at x=0 and x=2).

    So the domain is all values from -1 to 3 inclusive.

    Answer:

    Domain = [-1, 3]

    The RANGE of a function is all possible OUTPUT (y) values.

    So scan the function from bottom to top.

    The lowest value is y = -2 (with a solid dot)

    The highest value is y = 2 (with a solid dot)

    The various parts of the graph cover all values in between.

    So the range is all values from -2 to 2 inclusive.

    Answer:

    Range = [-2, 2]

    P.S. Regarding your answer as a range, you tried to show it as 3 different intervals. If you are going to do that you would need to say it is the *union* of those intervals. Also in interval notation you always show the smaller value in the interval first, then the larger value.

    So it seems you were looking to say:

    (1, 2] U [-1, 2) U [-2, 1)

    But you are listing overlapping intervals and you really just need to say from -2 to 2.

    Answer:

    Range = [-2, 2]

  • 3 weeks ago

    Domain is the possible input, x, values

    [-1, 3]

    Range is the possible output, y, values

    [-2, 2]

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