2.1 relations and functions

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2.1 relations and functions

  1. 1. 2-1: Functions & Their GraphsObjectives:• I will determine if a relation is a function.• I will determine domain and range of a relation from a graph, from a table, or from an equation with and without restrictions.
  2. 2. Relations & FunctionsRelation: a set of ordered pairsDomain: the set of x-coordinatesRange: the set of y-coordinatesWhen writing the domain and range, do not repeat values.
  3. 3. Relations and FunctionsGiven the relation: {(2, -6), (1, 4), (2, 4), (0,0), (1, -6), (3, 0)}State the domain: D: {0,1, 2, 3}State the range: R: {-6, 0, 4}
  4. 4. Relations and Functions• Relations can be written in several ways: ordered pairs, table, graph, or mapping.• We have already seen relations represented as ordered pairs.
  5. 5. Table{(3, 4), (7, 2), (0, -1), x y (-2, 2), (-5, 0), (3, 3)} 3 4 7 2 0 -1 -2 2 -5 0 3 3
  6. 6. Mapping• Create two ovals with the domain on the left and the range on the right.• Elements are not repeated.• Connect elements of the domain with the corresponding elements in the range by drawing an arrow.
  7. 7. Mapping{(2, -6), (1, 4), (2, 4), (0, 0), (1, -6), (3, 0)} 2 -6 1 4 0 0 3
  8. 8. Functions• A function is a relation in which the members of the domain (x-values) DO NOT repeat.• So, for every x-value there is only one y-value that corresponds to it.• y-values can be repeated.
  9. 9. Functions• Discrete functions consist of points that are not connected.• Continuous functions can be graphed with a line or smooth curve and contain an infinite number of points.
  10. 10. Do the ordered pairs represent afunction?{(3, 4), (7, 2), (0, -1), (-2, 2), (-5, 0), (3, 3)}No, 3 is repeated in the domain.{(4, 1), (5, 2), (8, 2), (9, 8)}Yes, no x-coordinate is repeated.

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