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IDENTIFYING FUNCTIONS Use your knowledge of functions to complete the table below. Identify whether or not...

IDENTIFYING FUNCTIONS
Use your knowledge of functions to complete the table below. Identify whether or not each representation is a function, and be sure to justify your answer.
REPRESENTATION | FUNCTION? | JUSTIFICATION
1. Table: x: −3, −1, 1, 3; y: 10, 2, 2, 10.
2. {(−9, 0), (−4, 5), (0, 9), (4, 5), (9, 0)}
3. [Graph of an ellipse centered at the origin.]
4. {(−3, 0), (13, 4), (6, 3), (13, −4), (22, 5)}
5. [Mapping diagram from X = {−1, 0, 1} to Y = {1, 0}; each element of X has one outgoing arrow.]
6. [Graph consisting of a decreasing line segment followed by an increasing ray, forming a V shape.]
7. Table: x: 25, 25, 36, 36; y: 5, −5, 6, −6.

Answer

  1. Yes, a function. Each x-value is paired with exactly one y-value. Different inputs may share an output.

  2. Yes, a function. Each input (−9, −4, 0, 4, 9) has exactly one output.

  3. No, not a function. The ellipse fails the vertical line test: some x-values correspond to two y-values.

  4. No, not a function. The input 13 has two different outputs, 4 and −4.

  5. Yes, a function. Each element of X has exactly one arrow pointing to an element of Y.

  6. Yes, a function. The graph passes the vertical line test: each x-value in its domain has exactly one y-value.

  7. No, not a function. The input 25 has outputs 5 and −5, and the input 36 has outputs 6 and −6.

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