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Math Pacing

Relations. Math Pacing. Find the coordinates of the vertices of the figure after the transformation is performed. 1. triangle MNP with M (1, 1), N (3, 2), P (2, 4) translated 3 units down and 5 units to the left.

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Math Pacing

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  1. Relations Math Pacing Find the coordinates of the vertices of the figure after the transformation is performed. 1. triangle MNP with M (1, 1), N (3, 2), P (2, 4) translated 3 units down and 5 units to the left. 2. A vertex of a triangle is found at point (x, y). Which ordered pair shows the coordinates of this vertex after a 90º rotation counterclockwise about the origin? M’ (– 4, – 2) N’ (– 2, – 1) P’ (– 3, 1)

  2. Relations A relation is a set of ordered pairs. A relation can be represented by a set of ordered pairs, a table, a graph or a mapping. A mapping illustrates how each element of the domain is paired with an element in the range. Relations

  3. x y 4 3 –2 –1 –3 2 2 –4 0 –4 Represent a Relation Example 3-1a Express the relation {(4, 3), (–2, –1), (–3, 2), (2, –4),(0, –4)} as a table, a graph and a mapping. Table List the set of x-coordinates in the first column and the corresponding y-coordinates in the second column.

  4. x y 4 3 –2 –1 –3 2 2 –4 0 –4 Represent a Relation Example 3-1a Graph Grapheach ordered pair on a coordinate plane.

  5. x y 4 3 –2 –1 –3 2 2 –4 0 –4 Represent a Relation Example 3-1b Mapping List the x values in set X and the y values in set Y. Draw an arrow from each x value in X to the corresponding y value in Y.

  6. x y 4 3 –2 –1 –3 2 2 –4 0 –4 Represent a Relation Example 3-1b Determine the domain and range. Answer: The domain for this relation is {–3, –2, 0, 2, 4}. The range is {–4, –1, 2, 3}.

  7. Represent a Relation Example 3-1c a. Express the relation {(3, –2), (4, 6), (5, 2), (–1, 3)} as a table, a graph, and a mapping. b. Determine the domain and range. Answer: Answer: D = {–1, 3, 4, 5};R = {–2, 2, 3, 6}

  8. Relations When graphing relations that represent real-life situations, you may need to select values for the x- or y-axis that do not begin with 0 and do not have units of 1. Relations

  9. Use a Relation Example 3-2a Opinion PollsThe table shows the percent of people satisfied with the way things were going in the U.S. at the time of the survey. Determine the domain and range of the relation. Answer: The domain is {1992, 1995, 1998, 2001}. The range is {21, 32, 51, 60}.

  10. Use a Relation Example 3-2b Graph the data. Thevalues of the x-axis need to go from 1992 to 2001. It is notpractical to begin the scale at 0. Begin at 1992 and extend to 2001 to include all of the data. The units can be 1 unit pergrid square. Thevalues on the y-axis need to go from 21 to 60. In this caseit is possible to begin the scale at 0. Begin at 0 and extend to 70. You can use units of 10.

  11. Use a Relation Example 3-2c What conclusions might you make from the graph of the data? Answer: Americans became more satisfied with the country from 1992-1998, but the percentage dropped from 1998-2001.

  12. Use a Relation Example 3-2d Endangered SpeciesThe table shows the approximate world population of the Indian Rhinoceros from 1982 to 1998. a.Determine the domain and range of the relation. Answer: D = {1982, 1986, 1990, 1994, 1998} R = {1000, 1700, 1900, 2100}

  13. Use a Relation Example 3-2d b. Graph the data. Answer:

  14. Use a Relation Example 3-2d c. What conclusions might you make from the graph of the data? Answer: The population of the Indian rhinoceros has been increasing since 1982.

  15. Relations The inverse of any relation is obtained by switching the coordinates in each ordered pair. Relation Q is the inverse of relation S if and only if for every ordered pair (a, b) in S, there is an ordered pair (b, a) in Q. Relations

  16. Inverse Relation Example 3-3a Express the relation shown in the mapping as a set of ordered pairs. Then write the inverse of the relation. RelationNotice that both 7 and 0 in the domain are paired with 2 in the range. Answer: {(5, 1), (7, 2), (4, –9), (0, 2)} InverseExchange X and Y in each ordered pair to write the inverse relation. Answer: {(1, 5), (2, 7), (–9, 4), (2, 0)}

  17. Inverse Relation Example 3-3b Express the relation shown in the mapping as a set of ordered pairs. Then write the inverse of the relation. Answer: Relation:{(3, 2), (–4, 1), (5, 2)}Inverse: {(2, 3), (1, –4), (2, 5)}

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