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Introduction to Functions: Understanding Relations, Outputs, and Notation

In this lesson, students will learn the foundational concepts of functions in mathematics. Key objectives include determining whether a given relation qualifies as a function and finding specific values using function notation. Students will explore how each input (x) corresponds to exactly one output (y), along with practical applications of the vertical line test to analyze graphs. Through examples and exercises, learners will build a solid understanding of functions, ensuring they can accurately interpret mathematical relations and perform function evaluations.

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Introduction to Functions: Understanding Relations, Outputs, and Notation

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  1. 10-2-13 Bellwork

  2. Bellwork solutions

  3. Lesson 2-6 (Intro to Functions)Objectives:The student will be able to: 1. To determine if a relation is a function. 2. To find the value of a function.

  4. 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

  5. Function Notation Input Name of Function Output

  6. 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!

  7. 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)}

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

  9. 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!

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

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

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

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

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

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

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