Relations are sets of ordered pairs that represent connections between elements. A relation is a function if each element in the domain (input) is uniquely mapped to an element in the range (output). This can be tested using the vertical line test - if a vertical line can pass through the graph of a relation more than once, it is not a function. The domain of a relation is the set of all first elements of each ordered pair, while the range is the set of all second elements. A relation is a function if its domain does not contain repeating elements.

1. Relations & Functions
Remediation Notes

2. Vocabulary
Relation
Domain
Range
Function
Vertical Line Test

3. What is a relation?
A relation is a set of ordered pairs.
{ }  means set
(1, 2), (-1, 3), (-2, -5)  are ordered pairs
Now put this together and you have…
{(1, 2), (-1, 3), (-2, -5)}  a RELATION!
Everything that is a set of points is a
relation…don’t let the word relation
confuse you.. especially on the EOC!

4. Domain INPUT
**The domain is the set of x values
What is the domain in the below relation?
{(1, 2), (-1, 3), (-2, -5)}
Domain: {1, -1, -2}

5. Range OUTPUT
**The range is the set of y values
What is the range in the below relation?
{(1, 2), (-1, 3), (-2, -5)}
Range: {2, 3, -5}

6. Functions
How can you tell if a relation is a function?
 Mapping
 Domain does NOT repeat values, but
range CAN
 Vertical Line Test

7. Functions
How can you tell if a relation is a function?
 Mapping
With mapping, we will check to see if every
value of x (Domain) has only one
mapping to a y value.

8. In Figure 1,
3 is mapped to 5
and 6…thus
making this NOT
A FUNCTION!

9. In Figure 2,
All values in the
domain are mapped
to different range
values…thus
making this A
FUNCTION!

10. Are Figures 3 & 4
Function?
Figure 3 is a
Function!
Figure 4 is NOT a
Function!

11. Functions
How can you tell if a relation is a function?
 Domain does NOT repeat values
{(1, 2), (-1, 3), (-2, -5)}
Is this a Function?
Do the x values repeat?
No, the x values do not repeat…thus, this IS A
FUNCTION!

12. Functions
How can you tell if a relation is a function?
 Domain does NOT repeat values
{(-1, 2), (-1, 3), (-2, -5)}
Is this a Function?
Do the x values repeat?
Yes, the x values do repeat…thus, this IS
NOT A FUNCTION!

13. Functions
How can you tell if a relation is a function?
 Vertical Line Test
A Vertical line goes in an
Up and Down direction.

14. Functions
How can you tell if a relation is a function?
 Vertical Line Test
Does a vertical line cross through
this graph more than once? 1
If so, then this relation 2
(graph) is NOT a function!
Not A
FUNCTION

15. Each graph to the
right
IS A
FUNCTION!
Notice the
vertical line?
It is only crossing
the graphs once
VERTICALLY!

16. Each graph to the
right
IS NOT A
FUNCTION!
Notice the
vertical line?
It is crossing
each of the
graphs more than
once
VERTICALLY!

17. You are now ready to
begin the Remediation
Assignment
Good luck!