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Objectives The student will be able to:

Learn how to determine if a relation is a function, find the value of a function, understand function notation, and apply the vertical line test. Gain insights into domain, range, and function characteristics with practical examples.

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Objectives The student will be able to:

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  1. ObjectivesThe student will be able to: 1. To determine if a relation is a function. 2. To find the value of a function

  2. Functions A function is a relation in which each element of the domain is paired with exactly one element of the range. Another way of saying it is that there is one and only one output (y) with each input (x). f(x) y x

  3. Function Notation Input Name of Function Output

  4. 2 3 5 4 3 0 2 3 f(x) f(x) f(x) f(x) Determine whether each relation is a function. 1. {(2, 3), (3, 0), (5, 2), (4, 3)} YES, every domain is different!

  5. 1 4 5 5 6 6 9 3 1 2 f(x) f(x) f(x) f(x) f(x) Determine whether the relation is a function. NO, 5 is paired with 2 numbers! 2. {(4, 1), (5, 2), (5, 3), (6, 6), (1, 9)}

  6. Answer Now Is this relation a function?{(1,3), (2,3), (3,3)} • Yes • No

  7. A relation assigns the x’s with y’s 1 2 2 4 3 6 4 8 10 5 Domain (set of all x’s) Range (set of all y’s) This relation can be written {(1,6), (2,2), (3,4), (4,8), (5,10)}

  8. 1 2 2 4 3 6 4 8 10 5 Set A is the domain Set B is the range Whew! What did that say? A function f from set A to set B is a rule of correspondence that assigns to each element x in the set A exactly one element y in the set B. A function f from set A to set B is a rule of correspondence that assigns to each element x in the set A exactly one element y in the set B. A function f from set A to set B is a rule of correspondence that assigns to each element x in the set A exactly one element y in the set B. No x has more than one y assigned All x’s are assigned This is a function ---it meets our conditions Must use all the x’s The x value can only be assigned to one y

  9. A good example that you can “relate” to is students in our maths class this semester are set A. The grade they earn out of the class is set B. Each student must be assigned a grade and can only be assigned ONE grade, but more than one student can get the same grade (we hope so---we want lots of A’s). The example show on the previous screen had each student getting the same grade. That’s okay. A good example that you can “relate” to is students in our maths class this semester are set A. The grade they earn out of the class is set B. Each student must be assigned a grade and can only be assigned ONE grade, but more than one student can get the same grade (we hope so---we want lots of A’s). The example shown on the previous screen had each student getting the same grade. That’s okay. 1 2 2 4 3 6 4 8 10 5 2 was assigned both 4 and 10 Is the relation shown above a function? NO Why not???

  10. Vertical Line Test (pencil test) If any vertical line passes through more than one point of the graph, then that relation is not a function. Are these functions? FUNCTION! FUNCTION! NOPE!

  11. Vertical Line Test FUNCTION! NO! NO WAY! FUNCTION!

  12. Answer Now Is this a graph of a function? • Yes • No

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