1. f(x) y x A function is a relation that gives a single
output number for every valid input number
(x values cannot be repeated).
A relation is a rule that produces one or more
output numbers for every valid input number
(x and y values may be repeated).
f(x) y x

2. x y 5 6 7 Relations and functions can be shown many different ways.
Are these relations or functions?
Function
&
Relation x y 1 2 3 4
x y 5 6 7 5 6 7
(1, 5), (2, 6), (3, 7), (4, 6)

3. Are these relations or functions?
Not a Function but a
Relation x y
x y 5 6
1 7
1 6 1 2 5 6 7

4. Are these relations or functions?x y
Not a function
But a relation 5 6 8 11 1 2 3
x y 5 6 11 8

5. These all represent the SAME function!
In words:
Double the number and add 3
As an equation:
y = 2x + 3
These all represent the SAME function!
As a table of values:
x y
-1 1
0 3
1 5
As a set of ordered pairs:
(-2, -1) (-1,1) (0,3) (1, 5) (2, 7) (3, 9)

6. Function Notation
Input
Name of Function
Output

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. 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

10. 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

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

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

13. 3(3)-2 3 7 -2 -8 3(-2)-2 Given f(x) = 3x - 2, find: 1) f(3) 2) f(-2)
= 7
3(3)-2 3 7
= -8
3(-2)-2 -2 -8

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

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

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