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basic concepts of Functions

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basic concepts of Functions

basic concepts of Functions

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  • 1. FUNCTIONS : DOMAIN AND RANGE
  • 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. 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. 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. 6 5 4 3 2 1 -6 -4 -2 2 4 -1 Domain:{all real numbers} Range:{y:y≥0} 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. 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. 2. 10 5 -10 10 20 -5 -10 Domain={x:x ≥ 3} Range:{all reals} -15
  • 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. 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}