Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

What is the domain and range of this graph?

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  • ?
    Lv 7
    1 month ago

    Domain: (-∞, -1)U(-1,1)U(1,+∞)

    Range: (-∞, -3)U(-3, -1)U(-1, +∞)

  • 1 month ago

    Domain is all possible "x" values that will result in a "y".  In this curve there are two gaps.  One at x = -1 (there's an open circle in the middle of the curve) and one at x = 1 where the limit as x approaches 1 from the left is ∞ and the a x approaches 1 from the right is -∞. 

    All other values of x result in a value for y so the domain here is:

    { x | x < -1 or -1 < x < 1 or x > 1 }

    or:

    { x | x ≠ -1 and x ≠ 1 }

    Both say the same thing.

    Range is the list of "y" values that result from the "x" values in the domain.

    The gap at x = -1 creates a gap at y = -1.

    And there's the mine at y = -3 where there are no data points for a similar reason why x = 1 had a gap.

    So we can write the range to be:

    { y | y < -3 or -3 < y < -1 or y > -1 }

    or:

    { y | y ≠ -3 and y ≠ -1 }

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