1. Fun With Functions!
By,
Sarah Lutsic

2. What is a Function?
• In a relationship of values, such that, for
every input X , there is exactly one output
Y.

3. Is this a function?
X Y X Y
1 3 1 4
2 8 2 7
4 7 1 5
5 3 3 9
YES NO

4. Vertical Line Test
-A test used to determine if a graph is a
function
-Can only pass through one point
-Pass: Function
-Fail: Not a function

5. Function?
Pass: Function
Fail: Not a function
Passes vertical line test; Fails vertical line test;
Function Not a function

6. Once we determine a
relationship is a function, we
can decide if it is …
-one to one
-onto

7. One-to-One
For every Y , there is
at most one X.

8. Is this function 1-1?
X Y
1 8
2 7
3 6
8 3
5 9
YES

9. Is this function 1-1?
(1,3) (4,5) (7,3)
X Y
1
3
4
5
7
7
Not a function because 1 and 7 both
map to 3.

10. Is this function still 1-1?
X Y
E1 3
2 9
4 6
5 8
12
YES, a 1-1 function does not need
to map to every Y.

11. Horizontal Line test
-Test used to determine if a graph is 1-
1
-Can only pass through one point
-Pass: The function is 1-1
-Fail: The function is not 1-1

12. Is this graph 1-1?
YES NO

13. Onto
For every Y , there is
at least one X.

14. Is this function onto?
X Y
1 2
3 4
5 6
7
YES, each x maps to AT LEAST
one y value.

15. Onto?
X Y
1 5
2 6
3 7
4 8
NOT onto because nothing is being
mapped to 8.

16. Work Cited
Graphs on slide 5:
http://www.ltcconline.net/greenl/courses/152a/
keys/Exam310/exam3w10key.htm
Graphs on slide 12:
http://algebra.freehomeworkmathhelp.com/Rel
ations_and_Functions/relations_and_function
s.html