1. Unit 2.1 What is a Function?

2. f(x) y x Unit 2.1 What is a Function?
Thur
09/03
Unit 2.1 What is a Function?
What is a function?
Mathematical equations that assign unique outputs to given inputs.
f(x) y x

3. Unit 2.1 What is a Function? Everyday Functions ... Thur 09/03

4. Thur
09/03
Unit 2.1 What is a Function?
What is a relation?
Any set of ordered pairs that share a known relation.
Examples: (x,y)
(2,0)
(1,4)
(4,-2)
(3,-1)

5. Unit 2.1 What is a Function? x y Input Output Domain Range
Thur
09/03
Unit 2.1 What is a Function?
The set of all first components (x) of the order pairs of the function or relation
The set of all second components (y) of the order pairs of the function or relation.
What is a domain?
What is a range? x y
Input
Output
Domain
Range

6. f(x) y x Unit 2.1 What is a Function?
Thur
09/03
Unit 2.1 What is a Function?
A relation in which each element of the domain (x) is paired with exactly one element of the range (y).
Another way of saying it is that there is one and only one output (y) with each input (x).
What
defines a
Function?
f(x) y x

7. Unit 2.1 What is a Function? Input Name of Function Output Thur 09/03
Notation
Input
Name of Function
Output

8. Is the data set a function?
Unit 2.1 What is a Function?
Thur
09/03
Is the data set a function?
{(2, 3), (3, 0), (5, 2), (4, 3)}
f(x) 2 3
f(x) 3
f(x) 5 2
f(x) 4 3
YES, every domain is different!

9. Is the data set a function?
Unit 2.1 What is a Function?
Thur
09/03
{(4, 1), (5, 2), (5, 3), (6, 6), (1, 9)}
Is the data set a function?
f(x) 4 1
f(x) 5 2
f(x) 5 3
f(x) 6
f(x) 1 9
NO, 5 is paired with 2 numbers!

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

11. 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!

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

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

14. 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

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

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

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