A2 Domain and Range

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A2 Domain and Range

  1. 1. Domain and Range Algebra 2
  2. 2. Domain and Range <ul><li>The domain of a relation is the set of all inputs . </li></ul>
  3. 3. Domain and Range <ul><li>The domain of a relation is the set of all inputs . </li></ul><ul><li>The range of a relation is the set of all outputs . </li></ul>
  4. 4. 9 10 7 8 5 6 3 4 1 2 Output Input
  5. 5. Domain <ul><li>The domain of all polynomial functions is all Real numbers . </li></ul>
  6. 6. Domain <ul><li>The domain of all polynomial functions is all Real numbers . </li></ul>
  7. 7. Domain <ul><li>The domain of all polynomial functions is all Real numbers . </li></ul><ul><li>Radical functions cannot have a negative number under the radical . </li></ul>
  8. 8. Domain <ul><li>The domain of all polynomial functions is all Real numbers . </li></ul><ul><li>Radical functions cannot have a negative number under the radical . </li></ul><ul><li>Rational functions cannot have a zero in the denominator . </li></ul>
  9. 9. Set Notation <ul><li>All Real Numbers: </li></ul><ul><ul><li> </li></ul></ul><ul><ul><li>(-  ,  ) </li></ul></ul><ul><ul><li>{x | -  < x <  } </li></ul></ul>
  10. 10. Set Notation <ul><li>All Real Numbers except 2 and -2: </li></ul><ul><ul><li>(-  , -2)  (-2, 2)  (2,  ) </li></ul></ul><ul><ul><li>{x | x  -2, x  2} </li></ul></ul>
  11. 11. Set Notation <ul><li>All Real Numbers greater than or equal to 2: </li></ul><ul><ul><li>[2,  ) </li></ul></ul><ul><ul><li>{x | x  2} </li></ul></ul>
  12. 12. Set Notation <ul><li>All Real Numbers between -2 and 4: </li></ul><ul><ul><li>(-2, 4) not including </li></ul></ul><ul><ul><li>{x | -2 < x < 4} </li></ul></ul><ul><ul><li>[-2, 4] including </li></ul></ul><ul><ul><li>{x | -2  x  4} </li></ul></ul>
  13. 13. Set Notation <ul><li>All Real Numbers beyond -2 and 4: </li></ul><ul><ul><li>(-  , -2)  (4,  ) not including </li></ul></ul><ul><ul><li>{x | x < -2, x > 4} </li></ul></ul><ul><ul><li>(-  , -2]  [4,  ) including </li></ul></ul><ul><ul><li>{x | x  -2, x  4} </li></ul></ul>
  14. 14. Range <ul><li>To find the range of a function, think about the graph. </li></ul><ul><li>What values of the y-axis are included in the graph? </li></ul>
  15. 15. Graphing Calculator

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