1. Bell Ringer What quadrant will you find the following points in:
(3, 2)
(-4, -9)
(123, -21.5)
(-98, -22)
(4892, -1)
(-974, 0)
(0, 0)

2. Relations and Functions
Mr. Haupt
CC B.2

3. Relation
A relation is a set of ordered pairs. For example, the table below form a relation between age and height.
Age (years) 10 12 14 16 18 20
Height (feet) 4
4.5 5
5.5 6
6.2

4. Relations
You can list the set of ordered pairs in a relation using braces.
[(10, 4), (12, 4.5), (14, 5), (16, 5.5), (18, 6), (20, 6.2)]
These points can then be plotted on a graph to see how the values are related.
Another way to look at it is using a table map…

5. Table Maps
Back in Chapter 1, we learned that in order for a relation to be a function, there can only be exactly one output (range) for each input (domain).
List the domain and range values in order, and draw arrows from the domain to their range values.

6. Example Table Map Determine if this relation is a function:
[(11, -2), (12, -1), (13, -2), (20, 7)] 11 12 13 20 -2 -1 7

7. Example 2 Determine if the relation is a function:
[(-2, -1), (-1, 0), (6, 3), (-2, 1)] -2 -1 6 -1 1 3

8. Vertical Line Test
An easy way to tell if a relation is a function is by using the vertical line test.
If you can draw a vertical line that touches two or more points on a line, it is not a function.

9. Examples

10. Examples

11. Function Rule Tables
Function Rule Tables are simply plugging given values into a function to determine the range.
For example:
Evaluate the function rule f(a) = -3a + 5 for the domain {-3, 1, 4} a
-3a + 5
f(a) -3
-3(-3) + 5 14 1
-3(1) + 5 2 4
-3(4) + 5 -7

12. Example 2
Evaluate the function rule f(x) = x2 + 1 for the domain {-2, 0, 5}