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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. 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)}

Answer

  1. Yes, a function. Each x-value corresponds to exactly one y-value. Different inputs may have the same 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 vertical lines intersect it twice, so some x-values have two y-values.

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

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