basic concepts of Functions

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basic concepts of Functions

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basic concepts of Functions

  1. 1. FUNCTIONS : DOMAIN AND RANGE
  2. 2. Domain: In a set of ordered pairs, (x, y), the domain is the set of all x-coordinates. Range: In a set of ordered pairs, (x, y), the range is the set of all y-coordinates.
  3. 3. The set of ordered pairs may be a limited number of points. Given the following set of ordered pairs, find the domain and range. Ex:{(2,3),(-1,0),(2,-5),(0,-3)} Domain: {2,-1,0} Range: {3,0,-5,-3} If a number occurs more than once, you do not need to list it more than one time.
  4. 4. The set of ordered pairs may be an infinite number of points, described by a graph. 6 5 Given the following graph, find the domain and range. 4 3 2 1 -6 -4 -2 2 -1 4
  5. 5. 6 5 4 3 2 1 -6 -4 -2 2 4 -1 Domain:{all real numbers} Range:{y:y≥0} 6
  6. 6. The set of ordered pairs may be an infinite number of points, described by an algebraic expression. Given the following function, find the domain and range. Example: f (x) = x−5 Domain: {x: x≥5} Range: {y: y≥0}
  7. 7. Practice: Find the domain and range of the following sets of ordered pairs. 1. {(3,7),(-3,7),(7,-2),(-8,-5),(0,-1)} Domain:{3,-3,7,-8,0} Range:{7,-2,-5,-1}
  8. 8. 2. 10 5 -10 10 20 -5 -10 Domain={x:x ≥ 3} Range:{all reals} -15
  9. 9. 3. f (x) = 3x − 4 Domain={all reals} 2 Range:{y:y≥-4} 2 4. f (x) = x Domain={x:x≠0} Range:{y:y≠0}
  10. 10. 5. x + y = 4 Domain={x: -2≤x≤2} 2 2 Note: This is NOT a Function! Range:{y: -2≤y≤2} 6. f (x) = 3(x − 1) + 2 Domain={all reals} Range:{all reals}

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