1. Lesson 5.3 What is a Function?

2. What is “rule” mean to you?
Come up with examples when a rule applies to certain situations
Examples:

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

4. Function Notation
Input
Name of Function
Output

5. Different ways of writing
f(x) = 4x or y = 4x + 6
f(3) = 4(3) or y = 4(3) + 6

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

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

8. Is this relation a function? {(1,3), (2,4), (3,3)}
Yes No X Y 1 3 2 4
Answer Now

9. Is this relation a function? {(2,3), (2,-4), (3,3)}
Yes No X Y 2 3 -4
Answer Now

10. 3(3)-2 3 7 -2 -8 3(-2)-2 Given f(x) = 3x - 2, find: 1) f(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
h(-3) = 30

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