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Objectives The student will be able to:

Learn how to determine relations as functions, find function values, and apply function notation through examples and explanations. Explore the concept of functions and their importance in mathematics. Practice identifying functions with vertical line tests and solving function problems. Improve your function skills with practical exercises and clear explanations.

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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. SOL: A.7aef Designed by Skip Tyler, Varina High School

  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. 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!

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

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

  10. Given f(x) = 3x - 2, find: = 7 1) f(3) 2) f(-2) 3(3)-2 3 7 = -8 3(-2)-2 -2 -8

  11. Given h(z) = z2 - 4z + 9, find h(-3) (-3)2-4(-3)+9 -3 30 9 + 12 + 9 h(-3) = 30

  12. Answer Now Given g(x) = x2 – 2, find g(4) • 2 • 6 • 14 • 18

  13. Answer Now Given f(x) = 2x + 1, find-4[f(3) – f(1)] • -40 • -16 • -8 • 4

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